1. Introduction why a Cimpa-Imamis School 2. Overview by langstonwalker

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									                         Report on Cimpa-Imamis School

                             on Mathematical Finance

                           Hanoi, April 24 to May 4, 2007

                          (Marc Diener and Huyên Pham)




1. Introduction: why a Cimpa-Imamis School
This school is one of the 3 schools that have been planned in the IMAMIS program.
This European program has its origin in a CIMPA school in 1998 organized in Ho Chi
Min City where Professor A. Piriou, now retired, met 10 Filipino mathematicians. To
respond to a demand of these Filipino mathematicians, the CIMPA and professor
Piriou asked professors F. and M. Diener to apply for an European project, accepted
in 2004. The project involves CIMPA through the organization of 3 schools, one in
each Asian partners, Malaysia, Vietnam and Philippines. For each of these 3 schools,
the EU financial participation is planned to cover 50% of the total cost. The Malaysian
school took place in Kuala-Lumpur in May 2006. This is the second school, the third
and last one will take place in Ateneo de Manila University in August 2007.


The chosen subjects are topic in Mathematical Finance relevant for teachers and
practitioners in Vietnam, Philippines, Malaysia, and other countries in East and
South-East Asia. They are topics taught by the lecturers chosen among the most
innovative lectures they give in their Master teachings in their home universities.

2. Overview
All lectures took place at the Institute of Mathematics, Hanoi (IMH);( the computer
sessions took place at an other location.)

The planned lecturers were

Nicole Elkaroui (Polytechnique), Giles Pagès (Paris 6), Santiago Carillio (Autonoma
de Madrid), Wolfgang Runggaldier (Padova, Italy), Francine Diener (Nice), Marc
Diener (Nice) and Huyên Pham (Paris 7), that, except for Mrs El Karoui that could
not come because of personal reason, all gave lectures. Finally, S. Carilio and G.
Pagès were assisted by Alberto Suarez and Jacques Printemps respectively, for
adding a computer oriented aspect of their lectures. All the talks have been given in
English, part with blackboard support part with video-LCD support. All lecturers also
provided hands-out of their lecture and all participants could get a copy of all the
computer files that had been prepared by the lecturers. The computer programmes
given used MatLab (Suarez) and SciLab (Printems)

Expected number of participants was Hanoi: 18, Vietnam (not from Hanoi): 12,
ASEAN (not from Vietnam): 13, EU (Lecturers): 8 . Finally, these numbers became
49 people from Hanoi, 14 from Vietnam outside of Hanoi, ASEAN (not in Vietnam)
22, and 8 lecturers. Obviously, the subject attracted many people.
The local Coordinator of the School was Nguyen Dinh Cong (Institute of
Mathematics, Hanoi, Deputy Director)




3. The purpose

 When the writer of these lines began his scientific life, the fact that probability was
part of Mathematics was still a matter of dispute; only few French mathematicians
were aware of the dramatic progress done in the theory of stochastic process,
martingale theory or stochastic integrals, and as a consequence, the teaching of
probability at high school was at the best related with combinatorics, or at the worse
pure magic.

At the beginning of the 1970’ a scientific revolution took place when Black and
Scholes (rediscovering results already known by Bachelier) introduced models for the
behaviour of stock markets in a way that was enough accurate to diminish
dramatically the risks on the so called market of derivatives (such as Put and Call
options), and Merton, Harrison and Pliska found out the importance of martingales in
modelling these markets, and how to turn the very convincing modelling tool called
“arbitrage” into effective mathematical models.

As a consequence, banks and financial institutions became places that would attract
the best mathematicians and would issue a demand of production and better
understanding of sophisticate new results of math. Moreover, the problem of hedging
risks on derivatives gave natural examples of Itô stochastic integrals and martingale
representation theorem. Any institution, including the State, that has to deal with
exchange rates or interest rates needs to have a full staff that masters the language
of martingales and computations of stochastic integrals, creating a demand of young
people to be taught these subjects. As usual, the only way for anyone to keep in
touch with the evolution of ideas in a subject is to produce oneself results (i.e. do
research) in order to enter the exchange process called scientific communication.

When CIMPA asked us to get interested in the Asia Link program of the EU (see next
section) it was obvious to us that math for finance could/should be an organising
center for a new impulse in higher order mathematics in South East Asia, as it both
involves new beautiful mathematics (martingale theory, stochastic calculus) and
existing domain of research (Numerical Methods). Moreover, this domain of
mathematical knowledge will be supported by the double demand of teaching and
applications, as explained above.


This school is part of the larger project IMAMIS that has been suggested by CIMPA
in 2002. This project, that has been worked out mostly by the Université de Nice
Sophia-Antipolis (UNSA) and the University of the Philippines (UP), is a training
programme for higher order education scholars, and devoted to the creation of 15
new courses in Applied Mathematics and Information Science. These courses build
up the knowledge delivered in a new pluridisciplinary masters programme that is
organised in three tracks (Mathematical Finance, Numerical Methods, Information
Science). It is funded by the Asia Link programme of EU. It is run in partnership with
Ateneo De Manila University, Universiti Kebangsaan Malaysia (UKM), Institute of
Mathematics Hanoi (IMH), Université de La Rochelle (ULR), Departimento di
Mathematica - Universita di Pisa (UniPisa), Universidad Autónoma de Madrid, and
Université Pierre et Marie Curie (Paris 6),

As usual in higher order teaching, we found it necessary, besides the creation of the
courses, to initiate a research process that would allow the teachers involved to get
access to the scientific communication in that domain and thus keep there knowledge
up to date after the end of the two-and-a-half years Asia Link support. In our mind,
the Cimpa schools are the ideal tool to allow this process.

4. The lectures

          1. M. Diener: Discrete-time models in finance (5h)
          2. F. Diener: Continuous-time models in finance and stochastic calculus
             (9h)
          3. S. Carrillo and A. Suarez: Operational risk: measurement and control
             (5h course + 4h computer)
          4. G. Pagès: Introduction to numerical methods in probability for finance
             (4h course + 3h computer)
          5. J. Printems: Introduction to numerical methods for partial differential
             equations in finance (4h course + 3h computer)
          6. W. Runggaldier: Interest rate modelling (9h)
          7. H. Pham: Portfolio management and option hedging (9h)


1. Discrete-time Models in Finance
          Marc Diener : University of Nice, diener@unice.fr
                   http://math1.unice.fr/~diener/

   1. Pricing European options in a Cox-Ross-Rubinstein Model. Risque neutral
      probability. Convergence of the CRR exact formula to the Black-Scholes limit.

   2. Pricing American options in a CRR Model. Hedging/superhedging


2. Continuous-time Models in Finance and Stochastic Calculus
            Francine Diener : University of Nice, diener@unice.fr
                        http://math1.unice.fr/~diener/



   1. Brownian motion, Heat equation, Black-Scholes model of stocks prices. Self
      financing portfolios, stochastic integrals, profit & loss.

   2. Ito formula, stochastic differential equations, options pricing in the Black-
      Scholes model. Delta hedge, vol dependance, limits of the B&S model.

   3. The martingal approach or arbitrage pricing theory.

   4. Arbitrage free and complet markets: the 2 fondamental theorems
3. Operational risk : measurement and control
             Santiago Carrillo : RiskLab, Madrid,

santiago.carrillo@uam.es
    http://www.risklab-madrid.uam.es/es/miembros.html

         Alberto Suarez : Universidad Autonoma Madrid,
alberto.suarez@uam.es
               http://www.risklab-madrid.uam.es/es/miembros.html


   I   What is operational risk: from thick fingers to rogue traders.
         1. basical concepts related to operational risk.
         2. the notion of economical capital.
         3. the Basel II framework for operational risk.
   II. Operational risk and Basel II: basic models.
         1. the basic indicator approach.
         2. the standard approaches.
         3. critical analysis of basic model
         4. a practical more advanced example: the internal measurement
             approach.

   III. Operational risk and Basel II: advanced models.
         1. The loss distribution approach.
         2. The choice for severity distribution (threshold effect and Extreme Value
            Theory).

              3. The frequency distribution.
              4. Puting all together: practical computing of economical capital (Panjer
                 algorithm, FFT and Monte Carlo simulation).

       IV.     Practical issues.
               1. using different thresholds
               2. using external data.
               3. taking into account dependence structure (copula and fat tails).


4. Introduction to numerical methods in probability for finance
                  Gilles Pagès : PMA, University Paris 6, gpa@ccr.jussieu.fr
                           http://www.proba.jussieu.fr/pageperso/pages


1. Simulation of random variables, variance reduction
   1.1 The fundamental principle of simulation and pseudo-random numbers
   1.2 The distribution function method
         Application to the simulation of exponential and Poisson distributions.
    1.3 The rejection method
         Application to the simulation of normal distributions.
    1.4 The Box-Muller method for normal vectors
         d-dimensional Normal vectors
         d-dimensional Gaussian vectors (with general covariance matrix).
    1.5 Application to the computation of Vanilla options pricing in a Black-Scholes
model by Monte Carlo.
              Premium.
         Greeks (sensitivity to the option parameters: an elementary approach).
    1.6 Variance reduction
        Control variate (optimization by on-line regression).
        Symmetrization.
         Importance sampling.
    1.7 Application to European option pricing II
        Option best match, call on exchange spread.
        Path-dependent options~I: Asian options.
        an example of stochastic volatility model: The Heston model.

2. Euler scheme of a Brownian diffusion
   2.1 Euler-Maruyama scheme
       Simulation
       Strong error rate
             Path-dependent options~II: Lookback and barrier options, first
           approach
   2.2 Milshtein scheme
   2.3 Weak error of the Euler scheme
            Main results for E(f(X_T)) : Talay-Tubaro Theorem, Bally-Talay
           Theorems
           Weak error for path-dependent functionals: the Brownian bridges
           method         Application to Path-dependent options~III: partial
           lookback and barrier options.
     Standard Romberg extrapolation and multistep Romberg extrapolation.

3. American options
    3.1 From American to Bermuda options
    3.2 Dynamic programming formula
        From arbitrage approaches Optimal stopping theory.
        Hedging.
    3.3 Numerical methods
        The Longstaff-Schwartz method.
        The optimal quantization tree approach.
                        On the computer... (3 hours)

4. Simulations on a computer

      The students will to compute by themselves some option pprices by Monte
      Carlo simulation.

   4.1 European option
               Compute by Monte Carlo the B-S vanilla Call, best match, exchange
      spread options as a function of the strike price, without and with control
      variate, with and without symmetriztion.
        Idem in a Heston model
        Barrier options
   4.2 American option (in 1-dimension)
       The Longstaff-Schwartz method.
       The optimal quantization tree approach.
5. Introduction to numerical methods for partial differential equations in
finance
               Jacques Printems: LAMA, University Paris 12, printems@univ-
              paris12.fr
     http://perso-math.univ-mlv/users/printems.jacques/

    1. Partial differential equations in mathematical finance
    1.1 Black-Scholes analysis
    Recall on the derivation of the Black-Scholes PDE
           1.2 Examples of some PDE’s occuring in finance with their typical
           features
          Through the Black-Scholes model :
           Large dimensions
           Degenerate PDE’s (Asian options, Lookback options)
           Need of numerical tools (no closed forms e.g. : call spread options)
           Bounded or unbounded domains (barrier options)
     1.3 Other methods
           Stochastic volatility models
           Heston’s models
    2. Finite difference methods for PDE’s
      2.1 Basis concepts
          Derivation of finite difference schemes. Accuracy
          Notion of stability (time). Explicit and implicit schemes
          Notion of stability (space). L^\infty-stability and discrete maximum principle
           Discretization in higher dimension
      2.2 Numerical implementation of BS type equation in 1-dimension.
          Numerical proof of the convergence. Numerical rate of convergence.
          Boundary conditions.
          Numerical smile.
      2.3 Numerical study of a 2-d stochastic volatility model : the Heston model
          Bring into play the numerical implementation. Sparse storage of the
          matrices. Comparison of different choices of discretization.
      2.4 Technique for reducing the dimension
          The alternate direction methods : example in a 2-d case
          The sparse grids
3. American options
    3.1 Different formulations
        The optimal stopping formulation
        The free boundary formulation
        The variational inequality formulation
    3.2 Semi-discretization in time and numerical methods
         Comparison of two methods (rate of convergence, efficiency) :
             Projected gradient method
             Howard’s method
4. Asian options
    4..1 Motivations
    4.2 PDE formulation and numerical scheme
         Rogers and Shi method
         Numerical implementation


5. Practical work

    5.1 European option
        Computation by Finite difference methods of the BS vanilla call in 1-d, best
match in 2-d, exchange spread in 2-d, options as a function of the strike price.
         Barrier options
   4.2 American option (in 1-dimension)
        The projected gradient method.
       The Howard method


6. Interest rate modeling
        Wolfgang Runggaldier : University of Padova,
        runggal@math.unipd.it
                 http://www.math.unipd.it/~runggal/


1. Bonds and Interest Rates;
2. Short Rate Models;
3. Martingale Models for the Short Rate;
4. Forward Rate Models;
5. Change of Numeraire;
6. LIBOR and Swap Market Models.




7. Portfolio management and option hedging
    Huyên Pham : PMA University Paris 7, and IUF, pham@math.jussieu.fr
           http://www.proba.jussieu.fr/pageperso/pham/


We present a review of concepts of utility theory and portfolio management in
financial markets, and show how stochastic control method are applied in this
context:

   1. Utility theory and risk aversion

   2. Dynamic programming and Bellman approach
       Merton’s portfolio/consumption choice, real options …
   3. Duality and martingale approach
      Mean-variance hedging
      Quantile hedging


Schedule

Monday 23 April 2007
8h00-9h30         Registration
9h30-10h00        Openning ceremony
10h00-10h15       break
10h15-12h00       M. Diener: Discrete-time models in finance I
Afternoon session
13h30-15h00       F. Diener: Continuous-time models in finance and stochastic
                  calculus I.
15h00-15h15        break
15h15-16h45        F. Diener: Continuous-time models in finance and stochastic
                   calculus II.

Tuesday 24 April 2007
8h00-9h45          M. Diener: Discrete-time models in finance II
9h45-10h00         break
10h00-12h00        S. Carrillo: Operational risk: measurement and control I
Afternoon session
13h30-15h00        S. Carrillo: Operational risk: measurement and control II
15h00-15h15        break
15h15-16h45         S. Carrillo: Operational risk: measurement and control III
Wednesday 25 April 2007
8h00-9h15          M. Diener: Discrete-time models in finance III
9h15-9h20          break
9h20-10h30         F. Diener: Continuous-time models in finance and stochastic
                   calculus IIIa.
10h30-10h40        break
10h40-12h00        F. Diener: Continuous-time models in finance and stochastic
                   calculus IIIb.
Afternoon session
13h30-15h30        A. Suarez: Operational risk I
15h30-15h45        Break
15h45-17h30        A. Suarez: Operational risk II
Thursday 26 April 2007
8h00-9h45          F. Diener: Continuous-time models in finance and stochastic
                   calculus IV.
9h45-10h00         break
10h00-12h00        F. Diener: Continuous-time models in finance and stochastic
                   calculus V.
Afternoon session
13h30-15h30        J. Printems: Introduction to numerical methods for partial
                   differential equations in finance I
15h30-15h45        Break
15h45-17h30        J. Printems: Introduction to numerical methods for partial
                   differential equations in finance II
Friday 27 April 2007
8h30-10h00         J. Printems: Introduction to numerical methods for partial
                   differential equations in finance III (computer work)
10h00-10h15        Break
10h15-11h45        J. Printems: Introduction to numerical methods for partial
                   differential equations in finance IV (computer work)
Afternoon session
13h30-14h30        G. Pagès: Introduction to numerical methods in probability for
                   finance I
14h30-15h00        Break
15h00-16h00        G. Pagès: Introduction to numerical methods in probability for
                   finance II
Saturday 28 April 2007
9h00-10h00         G. Pagès: Introduction to numerical methods in probability for
                   finance III
10h00-10h30        Break
10h30-11h30        G. Pagès: Introduction to numerical methods in probability for
                   finance IV

Afternoon session (92 Vinh Phuc street, Ba Dinh district, Ha Noi)
13h30-15h00        G. Pagès: Introduction to numerical methods in probability for
                   finance V (computer work)
15h00-15h15        Break
15h15-16h45        G. Pagès: Introduction to numerical methods in probability for
                   finance VI (computer work)
Wednesday 2 May 2007
8h15-9h45          H. Pham: Portfolio management and option hedging I
9h45-10h00         break
10h00-11h30        H. Pham: Portfolio management and option hedging II
Afternoon session
13h30-15h00        W. Runggaldier: Interest rate modelling I
15h00-15h15        Break
15h15-16h45        W. Runggaldier: Interest rate modelling II
Thursday 3 May 2007
8h15-9h45          W. Runggaldier: Interest rate modelling III
9h45-10h00         break
10h00-11h30        W. Runggaldier: Interest rate modelling IV
Afternoon session
13h30-15h00        H. Pham: Portfolio management and option hedging III
15h00-15h15        Break
15h15-16h45        H. Pham: Portfolio management and option hedging IV
Friday 4 May 2007
8h15-9h45          H. Pham: Portfolio management and option hedging V
9h45-10h00         break
10h00-11h30        H. Pham: Portfolio management and option hedging VI
Afternoon session
13h30-15h00        W. Runggaldier: Interest rate modelling V
15h00-15h15        Break
15h15-16h45        W. Runggaldier: Interest rate modelling VI
16h45-17h00        Closing of the School




5. Other activities
Tuesday 24 April: dinner at family Nguyen Van Duc’s Snake Restaurant in Gia Lam.
A delicious opportunity to taste seven different ways to enjoi snake meat and bones.
When arriving, participants could see the slaughtering of a snake, a dangerous and
not so easy task. This provided also a wonderful opportunity to visit a traditional
building

Monday 30 April and 1st of May are National holidays in Vietnam. This is why there
was no break on Wednesdays and that collective tourism was took place on these
days, together with Sunday.
Here an overview of this less scientific aspect of the School, that provided
nevertheless the opportunities of many discussions during the trips in bus, boats, and
walks through the National Parc.
       Sunday 29 April – Monday 30 April 2007
       Halong – Catba Island tour: bus to Haiphong, express-boat to Catba, walk through
       Catba National Parc: most came back completely soaked out by the rain but
       everybody was happy. Lunch at the Prince Hotel, swimming in the bay. Bus to the
       Noth of the island, where participants to place in dragon-shaped boats. The leave at
       sunset from Catba island will certainly one of the touristic climax of this tour that
       nobody will forget. Diner and night at the luxury Mithrin hotel. Next day, travel through
       the famous islands of Halong Bay with visit to one of the spectacular caves hidden in
       them. Visit to a small floating fish farms. See food on the boat heading back to
       Halong, bus travel back to Hanoi.

       Tuesday 1 May 2007
       City tour: Temple of Literature, Tran Quoc Pagoda and Bat Trang Pottery Village.
       The temple of Literature gave a good opportunity to get in touch with one of the
       origins of merit bases access to knowledge.

       Thursday 3 May: closing banquet at Nikko hotel. After the sumptuous dinner, several
       participants offered spontaneous song performances that enjoyed everybody.

       Friday 4 May 2007: Visit to Trang An Securities Joint Stock Company. This visit
       involved only three participants of the school: L u Hoàng     c, Francine Diener and
       Marc Diener. This gave us the opportunity to have a better understanding of the
       present (and rapidly changing) state of Securities exchanges in the country.




       6. List of Participants
       1. Participants

Nr Name                            Affiliation (in Vietnamese) Affiliation (in English)   Nationality
(i) Vietnamese participants
                                                               College of Natural
1                                                              Sciences, Vietnam
    Nguy n Th Thúy Anh              HKHTN Hà N i               National Univ.-Hanoi            VIETNAM
                                      i h c Bách Khoa Hà       Hanoi University of
2
    Nguy n Th Ng c Anh             n i                         Technology                      VIETNAM
                                                               Hanoi University of
3
    Tran Kim Anh                   DH Nong Nghiep I            Argiculture                     VIETNAM
                                                               Thai Nguyen
4
    T Qu c B o                        i h c Thái Nguyên        University                      VIETNAM
                                                               University of
5                                                              Economics, Hochiminh
    Ph m Trí Cao                      i h c Kinh t TPHCM       City                            VIETNAM
                                                               College of Natural
6                                                              Sciences, Vietnam
      ng ình Châu                     i h c KHTN Hà N i        National Univ.-Hanoi            VIETNAM
                                                               Foreign Trade
7
    Nguy n Trung Chính                i h c Ngo i Th     ng    University, Hanoi               VIETNAM
                                                               Institute of
8                                                              Mathematics,
    Nguy n   ình Công              Vi n Toán h c               Vietnamese Acad. Sci.           VIETNAM
                                                             & Tech.
                                   Tr ng Trung h c C s Nguyen Trai High
9
     Ngô Th Công                   Nguy n Trãi               School, Hanoi           VIETNAM
                                      i hoc Khoa h c T       College of Natural
10                                 nhiên -    i hoc Qu c gia Sciences, Vietnam
         V nC     ng               Hà N i                    National Univ.-Hanoi    VIETNAM
                                                             College of Economics,
11
     Ngô Kiên C      ng               i h c kinh t Hu        Hue University          VIETNAM
                                                             College of Natural
12                                                           Sciences, Vietnam
     Tr n M nh C         ng          HKHTN - HQGHN           National Univ.-Hanoi    VIETNAM
                                                             Duy Tan University,
13
     Nguy n Quang C           ng      i h c Duy Tân          Danang                  VIETNAM
                                                             Institute of
                                                             Mathematics,
14
                                                             Vietnamese Acad. Sci.
         Ng c Di p                 Vi n Toán h c             & Tech.                 VIETNAM
                                                             College of Natural
15                                    i h c KHTN- HQG Hà Sciences, Vietnam
     Nguy n Ti n D ng              N i                       National Univ.-Hanoi    VIETNAM
                                                             Institute of
                                                             Mathematics,
16
                                                             Vietnamese Acad. Sci.
     L u Hoàng       c             Vi n Toán h c             & Tech.                 VIETNAM
                                                             Institute of
                                                             Mathematics,
17
                                                             Vietnamese Acad. Sci.
   Tr n Anh   c                    Vi n Toán h c             & Tech.                 VIETNAM
18 Võ Th Trúc Giang                   I H C TI N GIANG Tien Giang University         VIETNAM
                                                             Institute of
                                                             Mathematics,
19
                                                             Vietnamese Acad. Sci.
     ng V Giang                    Vi n Toán H c             & Tech.                 VIETNAM
20 Nguy n Th Hà                       i h c Nha Trang        Nha Trang University    VIETNAM
                                                             College of Natural
21                                    i h c KHTN-DDHQG Sciences, Vietnam
     V Th Hi n                     Hà N i                    National Univ.-Hanoi    VIETNAM
                                                             Institute of
                                                             Mathematics,
22
                                                             Vietnamese Acad. Sci.
         V n Hi p                  Vi n Toán H c             & Tech.                 VIETNAM
                                                             Institute of
                                                             Mathematics,
23
                                                             Vietnamese Acad. Sci.
     D   ng M nh H ng              Vi n Toán h c             & Tech.                 VIETNAM
                                                             Hanoi University of
24
     Tr n Minh Hoàng                  i h c Bách khoa Hà n i Technology              VIETNAM
                                                             Academy of Finance,
25
         Th Thu H        ng        H c Vi n Tài Chính        Hanoi                   VIETNAM
                                   H c Vi n K thu t Quân Military Academy of
26
     Phan Th H       ng            s                         Technology              VIETNAM
                                                       Institute of
                                                       Mathematics,
27
                              H c viên Cao h c K13     Vietnamese Acad. Sci.
     Nguy n Th Mai H     ng   VTH                      & Tech.                 VIETNAM
                                                       College of Natural
28                            Khoa Toán-C -Tin h c, Sciences, Vietnam
     Nguy n V n H u             HKHTN                  National Univ.-Hanoi    VIETNAM
                              H c Vi n K thu t Quân Military Academy of
29
     Ph m V n Khánh           s                        Technology              VIETNAM
                                                       Vietnam Forest
30
     Ph m Quang Khoái            i h c Lâm Nghi p      University, Hà Tây      VIETNAM
                                                       Academy of Finance,
31
     Bùi Th Hà Linh           H c Vi n Tài Chính       Hanoi                   VIETNAM
                                                       Hanoi University of
32
     Ngô Hoàng Long             HSP Hà N i             Education               VIETNAM
                                                       National Economics
33
     Hoàng    c M nh             i h c Kinh t Qu c dân University, Hanoi       VIETNAM
                                                       Institute of
                                                       Mathematics,
34
                                                       Vietnamese Acad. Sci.
     Nguy n Quang Minh        Vi n Toán h c            & Tech.                 VIETNAM
                                                       College of Natural
35                               i h c Khoa h c t      Sciences, Vietnam
     Tr n Minh Ng c           nhiên                    National Univ.-Hanoi    VIETNAM
                                                       College of Natural
36                               i h c KHTN-Tp H Chí Sciences, Vietnam
   Bùi Nguy n Trâm Ng c       Minh                     National Univ.-HCMC     VIETNAM
37 Bùi Th Thanh Nhàn             i h c Quy Nh n        Quy Nhon University     VIETNAM
                              Tr ng       i hoc Kinh t Danang University of
38
         ng Th T Nh             à N ng                 Economics               VIETNAM
                                 i h c Hoa Sen Thành Hoa Sen University,
39
     Nguy n H ng Nhung        ph H Chí Minh            Ho Chi Minh City        VIETNAM
                                                       Institute of
                                                       Mathematics,
40
                                                       Vietnamese Acad. Sci.
     H     ng Phúc            Vi n Toán h c            & Tech.                 VIETNAM
                                                       Institute of
                                                       Mathematics,
41
                                                       Vietnamese Acad. Sci.
     T Duy Ph    ng           Vi n Toán h c            & Tech.                 VIETNAM
                                                       Thai Nguyen
42
     Tr n V n Quý               HThái Nguyên           University              VIETNAM
                              H c Vi n K thu t Quân Military Academy of
43
     Thi u Lê Quyên           s                        Technology              VIETNAM
                                                       Academy of Finance,
44
     Nguy n Th Thúy Qu nh     H c vi n Tài chính       Hanoi                   VIETNAM
                                                       School of Education,
45
     Nhan Anh Thai            Tr ng       i hoc C n Th Can Tho University      VIETNAM
                                                       University of
46                              H Kinh t TP H Chí      Economics, Hochiminh
     Nguy n H u Thái          Minh                     City                    VIETNAM
                                                           Institute of
                                                           Mathematics,
47
                                                           Vietnamese Acad. Sci.
   Tr n V n Thành               Vi n Toán h c              & Tech.                 VIETNAM
48 Lê V n Thành                     i h c Vinh             Vinh University         VIETNAM
                                                           Academy of Finance,
49
     Hoàng Ph    ng Th o        H c Vi n Tài Chính         Hanoi                   VIETNAM
                                                           Institute of
                                                           Mathematics,
50
                                                           Vietnamese Acad. Sci.
     Tr n Hùng Thao             Vi n Toán h c              & Tech.                 VIETNAM
                                                           College of Natural
51                                  i h c Khoa hoc T       Sciences, Vietnam
   Hoàng Ph ng Th o             nhiên                      National Univ.-Hanoi    VIETNAM
52 Ph m Minh Thông                  i h c Tây B!c          Tay Bac University      VIETNAM
53 Nguy n Th Th                     i h c Vinh             Vinh University         VIETNAM
                                                           Hanoi University of
54
     Nguy n Tu"n Thi n              i h c Bách Khoa        Technology              VIETNAM
                                                           Hanoi University of
55
     Nguy n Th Thanh Thu#           i h c S Ph m Hà N i Education                  VIETNAM
                                                           Institute of
                                                           Mathematics,
56
                                                           Vietnamese Acad. Sci.
     Hà Thành Trung             Vi n Toán h c              & Tech.                 VIETNAM
                                    i h c Bách Khoa Hà     Hanoi University of
57
     Tr n   ình Tu"n            N i                        Technology              VIETNAM
                                                           College of Financial
58                              Cao $%ng Tài chính K       Accounting, Quang
     Ph m Vi t Thanh Tùng       toán Qu ng Ngãi            Ngai                    VIETNAM
                                                           University of
59                                                         Economics, Hochiminh
     Tr n Gia Tùng                  i h c Kinh t TPHCM City                        VIETNAM
                                Cao $ ng cô)ng $ô&ng Ba& Community College of
                                         (
60
   Trâ&n    i&nh T ng
                   '            Ri)a Vu*ng Ta&u            Baria-Vungtau           VIETNAM
61 Tr n     ông Xuân                i h c C n Th           Can Tho University      VIETNAM
                                                           Institute of
                                                           Mathematics,
62
                                                           Vietnamese Acad. Sci.
     T ng Th Hà Yên             Vi n Toán h c              & Tech.                 VIETNAM
                                    i hoc Khoa h c T       College of Natural
63                              nhiên -     i hoc Qu c gia Sciences, Vietnam
     Nguy n Ti n Y t            Hà N i                     National Univ.-Hanoi    VIETNAM

(i) Non-Vietnam based participants
                                                      Ecole Polytechnique,
64 Nguyen Dinh Ha               Ecole Polytechnique
                                                      FRANCE                       VIETNAM
                                                      Institute of
                                                      Mathematics,
65 Doan Thai Son                Vien Toan Hoc
                                                      Vietnamese Acad. Sci.
                                                      & Tech.                      VIETNAM
66 Ha Huy Thai                  Economie mathématique Univ. Paris VI,              VIETNAM
                                                        FRANCE
                                                        Univ. Paris VI,
67 Nguyen Trung Lap           Univ. de Paris VI
                                                        FRANCE                        VIETNAM
                                                        University of the
                              University of the
68 Almocera S. Lorna                                    Philippines, Cebu City,   PHILIPPINES
                              Philippines, Cebu City
                                                        PHILIPPINES
                                                        Adventist University of
                              Adventist University of
69 Balila Edwin A                                       Philippines,              PHILIPPINES
                              Philippines
                                                        PHILIPPINES
                                                        Ateneo de Manilla
                              Ateneo de Manilla
70 Cabral Emmanuel                                      University, Quezon        PHILIPPINES
                              University, Quezon City
                                                        City, PHILIPPINES
                              University of Dhaka,      University of Dhaka,
71 Shafiqul Islam                                                                 BANGLADESH
                              Dhaka                     BANGLADESH
                                                        College of Science,
                              College of Science
72 Uyaco-Catinan Filame Joy                             Quezon City -             PHILIPPINES
                              Philippines
                                                        PHILIPPINES
                                                        School of Science and
                              Ateneo de Manilla
73 Tuprio Elvira                                        Engineering, Quezon       PHILIPPINES
                              University
                                                        City - PHILIPPINES
                                                        School of Science and
                              Ateneo de Manilla
74 Ramil Tagum Bataller                                 Engineering, Quezon       PHILIPPINES
                              University
                                                        City - PHILIPPINES
                                                        University of
75 Wee Oliver Ian             College of Science        Philippines, Quezon       PHILIPPINES
                                                        City - PHILIPPINES
                                                        Uinversity of Shanghai
                                                        for Science and
76 Gao Yan                    University of Shanghai                              CHINA
                                                        Technology, Shanghai
                                                        - CHINA
                                                        Prince of Songkla
                              Prince of Songkla
77 Saelim Rattikan                                      University, Pattani,      THAILAND
                              University, Pattani
                                                        THAILAND
                                                        Nakhonratchasima
                              Nakhonratchasima          Rajabhat University,
78 Hematulin Apichai                                                              THAILAND
                              Rajabhat University       Nakhonratchasima -
                                                        THAILAND
                                                        Suranaree University
                              Suranaree University of   of Technology, Muang
79 Sattayatham Pairote                                                            THAILAND
                              Technology                Nakhon Ratchasima -
                                                        THAILAND
                                                        Valaya Alongkorn
                              Valaya Alongkorn          Rajabhat University,
80 Kachin Goganutaporn                                                            THAILAND
                              Rajabhat University       Pathumthani –
                                                        THAILAND
                                                        University of Ruhuna,
81 Prasangika K.D.            University of Ruhuna                                SRI-LANKA
                                                        Matara, SRI-LANKA
                                                        University of Oslo,
82 Salleh Hassilah Binti      University of Oslo                                  MALAYSIA
                                                        NORWAY
                              Royal Academy of          Institute of Sc. and
83 Visal Hun                                                                      CAMBODIA
                              Cambdia                   Tech, Phnom Penh,
                                                                  CAMBODIA
                                                                  College of Science -
                                       Univ. of the Philippines   University of
84 Dakila Vine Villan                                                                    PHILIPPINES
                                       College                    Philippines, Quezon
                                                                  City - PHILIPPINES

        2. Lecturers

   Nr   Name                    Institutions                                         Nationality
   1    Marc Diener             University of Nice                                   FRANCE
   2    Francine Diener         University of Nice                                   FRANCE
   3    Santiago Carrillo       RiskLab, Madrid                                      SPAIN
   4    Alberto Suarez          Universidad Autonoma Madrid                          SPAIN
   5    Gilles Pagès            PMA, University Paris 6                              FRANCE
   6    Jacques Printems        LAMA, University Paris 12                            FRANCE
   7    Wolfgang Runggaldier    University of Padova                                 ITALY
   8    Huyên Pham              PMA University Paris 7, and IUF                      FRANCE

        3. Invited guest participant

        Milagros P. Navarro
        Department of Mathematics,
        University of the Philippines
        Diliman, Quezon City 1101
        PHILIPPINES

        4. Vietnamese invited guests

           1. Prof. Nguy n Khoa S n, Vice-President of VAST
           2. Prof. Ngô Vi t Trung, Director of Institute of Mathematics
           3. Prof. Lê Tu"n Hoa, Deputy Director of Institute of Mathematics
           4. Prof. Hà Huy Khoái, Former Director of Institute of Mathematics
           5. Prof. Hoàng Xuân Phú, Vice-Chairman of the Scientific Council of Institute of
              Mathematics
           6. Prof. Nguy n H u D , Dean of Math. Department of Hanoi University of
              Sciences
           Prof. Nguy n Vi t D ng, Deputy Director of Institute of Mathematics




        7. What will be the follow up to the school ?
        We received many reaction of participants expressing the fact that thanks to this
        school they understand now that sophisticate mathematics were needed in modern
        finance.

        For those who were already conscious of this evolution this school was a good
        occasion to see how the most recent topics in finance can be taught at Master level.
        This gave all the opportunity to build up collaboration schemes. This has already
        produced an partnership in applying for an Erasmus Mundus Action 4 proposal
submitted to the European Commission. If it is accepted, ti will allow new meetings in
the near future.

This school will also influence the teaching of applied math in the represented
countries in the spirit of the Internations Master in Apllied Mathematics and
Information Sciences (Imamis).

Thanks to a ForMath Vietnam, several Vietnamese Master students in Europ had the
opportunity to have a contact with their home institutions. This school helped them to
understand the importance of keeping on studying at a higher level and to engage
themselves in a Doctorat programme.

Finally, this school will promote the research on mathematical Finance at the
Department of Probability and Statistics of the Institute of Mathematics in Hanoi, as
well as collaboration with other academic and educational institutions in Vietnam

								
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