"1. Introduction why a Cimpa-Imamis School 2. Overview"
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, firstname.lastname@example.org 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, email@example.com 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, firstname.lastname@example.org http://www.risklab-madrid.uam.es/es/miembros.html Alberto Suarez : Universidad Autonoma Madrid, email@example.com 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, firstname.lastname@example.org 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, email@example.com 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, firstname.lastname@example.org 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