notes2 by shimeiyan


									Math 477 / 568 Casualty Actuarial Mathematics
Fall 2009 University of Illinois at Urbana-Champaign Professor Rick Gorvett
Session 2: Risks and Risk Theory

August 27, 2009

What Did We Discuss Last Time?
• What an actuary is, in words and numbers • What actuaries have traditionally done • What actuaries are doing, and starting to do, these days • What the P/C insurance market looks like

Today’s Agenda
• • • • • • • • • Vocabulary Actuarial science vs. finance Elements of an insurable risk Risk management functions, objectives, and techniques Contract law Insurance contract provisions Types of insurance coverages (summaries provided for your information) Adverse selection Risk theory and insurer solvency


We First Must Learn to Quack
Vocabulary is sometimes troublesome in practice. E.g, here are two words with multiple meanings

• “Risk”: sometimes used to mean
– Uncertainty – An entity exhibiting uncertainty (e.g., policyholder)

• “Loss”: sometimes used to mean
– An event causing damage or injury – A policyholder claim – A dollar amount associated with damage or injury

Some Foundational Vocabulary
• Risk: uncertainty concerning loss (occurrence, amount) • Objective risk: variation of actual relative to expected loss
– Law of Large Numbers: as the number of exposures increases, loss experience can be predicted more accurately

• Subjective risk: perception of risk or uncertainty – i.e., by an individual observer

Some Foundational Vocabulary (cont.)
“Risk is synonymous with uncertainty – lack of knowledge.”
- Irving Fisher, The Theory of Interest, 1930

“But Uncertainty must be taken in a sense radically distinct from the familiar notion of Risk, from which it has never been properly separated.”
- Frank Knight, Risk, Uncertainty, and Profit, 1921

“The term „risk,‟ as loosely used in everyday speech and in economic discussion, really covers two things which, functionally at least, in their causal relations to the phenomena of economic organization, are categorically different…. The essential fact is that „risk‟ means in some cases a quantity susceptible of measurement, while at other times it is something distinctly not of this character…. It will appear that a measurable uncertainty, or „risk‟ proper, as we shall use the term, is so far different from an unmeasurable one that it is not in effect an uncertainty at all. We shall accordingly restrict the term „uncertainty‟ to cases of the non-quantit(at)ive type.”
- Knight, ibid

Some Foundational Vocabulary (cont.)
• Chance of loss: probability of a specified event occurring
– Probabilities can be objective or subjective – A different concept than “risk”

• Peril: a cause of loss
– E.g., fire, earthquake, windstorm,… – For example, an insurance policy may cover losses from “all perils” (except those specifically excluded) or “named perils”

Some Foundational Vocabulary (cont.)
• Hazard: a physical or “emotional” condition that increases (or even creates) the chance of loss (frequency and/or severity)
Physical hazard: e.g., icy roads, defective wiring Moral hazard: dishonesty or character defects that increase loss frequency or severity Morale hazard: carelessness or indifference to loss because of existence of insurance

Some Foundational Vocabulary (cont.)
• Pure risk: involves only the possibilities of loss or no loss
– No possibility of gain – Often one can protect against pure risks through insurance or another risk financing mechanism

• Speculative risk: involves the possibilities of loss, no loss, or gain
– E.g., gambling – Generally, not considered insurable

Types of Pure Risks – Often Insurable
• Personal risks: risks that directly affect an individual
– E.g., death, sickness, unemployment

• Property risks: risks involving damage to or theft of property
– E.g., direct loss, indirect loss

• Liability risks: risks involving bodily injury or property damage to another person
– Generally no upper limit; legal defense costs

Actuarial Science versus Finance

Bühlmann’s Classification
Actuaries are of three kinds • Actuaries of the first kind: life
– Deterministic calculations

• Actuaries of the second kind: casualty
– Probabilistic methods

• Actuaries of the third kind: financial
– Stochastic processes

Actuaries vs. Financial Economists
Similarities • Technical, quantitative skills • Risk considerations • Specialized vocabulary • Address monetary issues

Actuaries vs. Financial Economists
Differences • Approach to risk • Approach to interest rates • Approach to profitability • Bases of valuation

Insurance vs. Finance Risk
Insurance • Pure risk
– Loss or no loss – No gain

Finance • Speculative risk
– Loss or no loss or gain/profit

• Law of large numbers
– More exposures ==> more accurate predictions

• Portfolio risk
– Diversification potential

Insurable Risks

Requirements of an Insurable Risk
• Large number of exposure units
– Preferably, very similar – Allows for law of large numbers

• Accidental loss
– Outside control of insured – Moral hazard issues – Randomness ==> law of large numbers

Requirements of an Insurable Risk (cont.)
• Losses are determinable and measurable
– Definite as to cause, place, time, and amount

• Losses not catastrophic
– Not a large proportion of exposure units – Pooling wouldn‟t work – Underwriting tools -- e.g.:
• Geographic spread • Reinsurance

Requirements of an Insurable Risk (cont.)
• Calculable chance of loss
– Frequency – Severity

• Economically feasible premium
– Affordable – Small relative to policy limit

Requirements of an Insurable Risk (cont.)
• Which of the following are insurable risks?
– War
– Unemployment

– Catastrophic meteor strike – Jobs re-training program

Key Types of Insurable Risks
• Property
– Direct property damage – Loss of use – Business interruption

• Liability
– Damage / injury to others
• From ownership (e.g., of car, home, business) • From personal activities • From professional activities

• Life
– Protect family – Protect business

• Health

Types of Insurance
• Private
– Life and health – Property-casualty
• Lines of business • Reinsurance
Fire Inland marine Ocean marine Personal auto Commercial auto Homeowners Commercial multi-peril Commercial liability Workers compensation ….

• Government
– Social
• Social security • Unemployment

– Other

Insurance and Risk Management

Functions of Insurance
• Risk-bearing and risk-pooling
– Transfer risks to insurer (for premium)
– Insurer diversifies by pooling

• Financial intermediation
– Issue debt contracts, and invest funds
– Compensation through yield spreads

– Economic value from market imperfections

Benefits of Insurance to Society
• • • • • Indemnification “Good night‟s sleep” Investment funds Loss prevention Enhancement of credit

Costs of Insurance to Society (the “dark side”)
• Cost of doing business
– Expenses

• Fraud • Inflated claims

Methods Of Handling Risks
• Insurance is only one way of addressing risk • Methods of managing risk:
– Avoid the risk in the first place – Control the frequency or severity of loss
• Loss prevention; loss reduction

– Retain the risk
• Active vs. passive retention

– Transfer the risk via non-insurance mechanisms
• Contractual transfer; hedging

– Transfer the risk via insurance mechanisms

Risk Management: Steps in the Process
• Determine the corporation‟s objectives
• Identify the risk exposures

• Quantify the exposures • Assess the impact • Examine financial risk management tools • Select appropriate risk management approach • Implement and monitor program

Risk Management Objectives
• Pre-loss objectives
– Economy – Reduction of worry / anxiety
• I.e., get a “good night‟s sleep”

– Meet externally imposed obligations / requirements – Social responsibility

Risk Management Objectives (cont.)
• Post-loss objectives
– – – – – Survival of the organization Uninterrupted operations Earnings stability Continued growth Social responsibility

Risk Management Objectives (cont.)
• Issues and conflicts
– Relationship of objectives to general corporate goals and objectives – Relationship to financial theory
• Value maximization

– Conflicts between the objectives themselves

Risk Management Techniques
Risk Control Reduce frequency and / or severity of potential losses • Avoidance
– Never take on the exposure in the first place – Abandon the exposure if already have it

• Loss control
– Change characteristics of the exposure – Attempt to reduce both frequency and severity

• Separation • Combination (pooling)

Risk Management Techniques (cont.)
Risk Financing Post-loss funding • Retention
– For non-serious, highly-predictable losses – What should retention level be? – How should losses be paid?
• • • • No advance funding Earmarked accounts Captive insurers Risk retention groups

Risk Management Techniques (cont.)
Risk financing (cont.) • Non-insurance transfers
– Contracts – Leases – Hold-harmless agreements

• Insurance
– – – – Voluntary vs. mandatory Deductibles Issues: Excess insurance - Price Selection of insurer - Service
- Solidity

Contract Law and Insurance Contracts

Requirements Of A Contract
• Offer

• Acceptance • Consideration • Legally competent parties • Legal purpose

Insurance Contracts – Special Characteristics
• Aleatory contract
– Contractual exchange may be unequal in value – Contingent on the occurrence / non-occurrence of a specific event

• Unilateral contract
– A legally enforceable promise is made by just one party

• Conditional contract
– There are qualifications on the insurer‟s promise

Insurance Contracts – Special Characteristics (cont.)
• Personal contract
– Contract is between the insurer and insured – Property/casualty policies generally cannot be “assigned” to others (although life policies can)

• Contract of adhesion
– Contract is generally written by just one of the parties (the insurer) – Thus, any ambiguities in the contract are generally resolved against the insurer

Other Insurance Concepts
• Indemnity
– Restore insured to (financial) condition before the loss – Purpose of “indemnity” principle:
• Do not allow the insured to profit • Reduce moral hazard

– Actual Cash Value (ACV) – Exceptions:
• Valued policies • Replacement cost coverage • Life insurance

Other Insurance Concepts (cont.)
• Insurable interest
– Insured has an “insurable interest” if suffers in event of a loss – Life insurance: required at contract inception – P/C insurance: required at time of loss

• Subrogation
– The insured‟s right to recover against another (responsible) party is transferred to the insurer

Elements of an Insurance Contract
• (Application)
– Applicant requests and offers to buy coverage – Insurer accepts or rejects the request

• (Binder)
– Temporary agreement providing coverage

• Declarations
– Identifies the insured and critical information – Describes coverage in broad terms

Elements of an Insurance Contract (cont.)
• Definitions

• Insuring agreement(s)
– Summarizes major promises agreed to – Named-perils: only specifically named perils are covered by the policy – All-risks: policy covers any losses unless from a peril which is specifically excluded

Elements of an Insurance Contract (cont.)
• Exclusions and exceptions
– Reasons for exclusions:
• Perils are uninsurable (refer back to requirements of an insurable risk) • Avoid duplication of coverage • Coverage is not typically needed

• Conditions
– Identifies the duties of the insured

Elements of an Insurance Contract (cont.)
• Miscellaneous
– Relationships among insurer / insured / third parties – E.g., cancellation, subrogation

• Endorsements (P/C) and riders (life)
– Change the provisions of the original policy

• Insured retains “first” part of loss • Purposes of deductibles:
– Eliminate small claims – Reduce premiums – Reduce moral / morale hazard

• Types of deductibles:
– – – – Straight Aggregate Franchise Disappearing

• Versus self-insured retentions (SIRs)

• In health insurance: insured and insurer split responsibility for losses on a percentage basis (e.g., 20 / 80) • In property insurance: gives insured an incentive to insure property for at least a certain amount
– “Insurance-to-value” – If insufficient coverage is purchased, insured must share in the loss

• Criminal law
• Wrongs against society

• Breach of contract • Torts – wrongs against others
– Intentional
• Assault, battery, trespass, slander

– Absolute / strict
• Liability imposed regardless of negligence / fault • Manufacturing explosives, owning dangerous animals

– Negligence
• Failure to exercise a legal standard of care

Elements of Negligence
• A legal duty to act (or not act) in a way that protects others from harm

• Breach of that duty • Damage or injury to the one owed the duty • Causal relationship (“proximate cause”) between the breach and the injury

Types of Damages
• Special damages
– “Economic” damages – Clearly determined and measured
• Medical expenses • Property damage • Loss of earnings

• General damages
– Cannot be specifically measured
• Pain and suffering • Loss of companionship

• Punitive damages
– Intended to punish or deter

Defenses Against Negligence
• Assumption of risk

• Contributory negligence • Comparative negligence • Last clear chance • Sovereign immunity

Insurance Coverages

Quick Summaries of Some Coverages
• Personal
– – – – Auto (liab & phys dam) HO (liab & property) Inland marine Umbrella

• Commercial
– – – – – – – – – – – General liability Business income Commercial multi-peril Businessowners Workers compensation Commercial auto Professional liability Boiler & machinery Marine (ocean & inland) Title Umbrella

• Government
– Federal flood insurance – FAIR plans – Fed. crop insurance

Personal Auto
• Liability coverage
– BI: bodily injury – PD: property damage – Split versus combined single limits (CSL)

• Medical payments coverage • Uninsured / underinsured motorists coverage • Physical damage (coverage for damage to “your” auto)
– Collision – Comprehensive (other than collision)

• Various policy forms – e.g.,
– HO-3: special form (very common) – HO-4: contents (for renters) – HO-6: condominium owners

• Section I: property coverages
– – – – Dwelling Other structures Personal property Loss of use

HO-3 policy form

• Section II: liability coverages
– Personal liability – Medical payments to others

Personal Inland Marine
• Protection for property subject to movement • Can tailor coverage to specific nature of property • Can get higher limits than in HO policy • Generally, coverage is worldwide • Personal Articles Floater (PAF)
– E.g., can cover jewelry, furs, silverware, golf equipment, fine arts, stamp / coin collections

• Scheduled Personal Property Endorsement

Personal Umbrella
• Protection against catastrophic lawsuit or judgment • Typically, $ 1-10 million liability limits • Two coverages:
– Excess liability insurance: applies on top of (in addition to) underlying coverage (e.g., auto and HO) – Other coverage: covers certain losses not covered by underlying policies (after deductible or selfinsured retention)
• E.g., personal injury: libel, slander,…

Federal Property Insurance Programs
• Certain types of perils are difficult for private insurance companies to insure – at least at affordable premiums • Examples:
– Flood insurance in flood zones – Property insurance in riot-prone areas – Crop insurance

• For each of these, the government got into the insurance business

Federal Flood Insurance
• Problems in flood-prone areas
– Potentially catastrophic loss – Adverse selection

• 1968 National Flood Insurance Act
– Provide insurance in flood zones – At subsidized rates

• 1983 Write-Your-Own Program
– Private insurers write the business – Backed up by federal government

FAIR Plans
• FAIR: Fair Access to Insurance Requirements • Property insurance: difficulties due to urban riots • 1968 Urban Property and Reinsurance Act • Make property insurance available to urban property owners unable to obtain coverage in normal markets • 31 states • Pool / syndicate
– Operated by private insurers – Private insurers share in program loss experience

Federal Crop Insurance
• Losses to crops – e.g., hail, wind, drought, excessive rain, plant disease • Catastrophic crop insurance:
– Guarantees 50% of average yield – Indemnified at 60% of expected market price

• Multiple-peril crop insurance
– 65% or 75% yield guarantee – Can elect up to 100% of expected market price

General Liability
• Exposures
– Premises and operations
• Premises: ownership and maintenance • Operations: on or off premises

– Products and completed operations liability – Contractual liability – Directors and officers liability

Commercial General Liability (CGL) Loss Dates
• Occurrence policy
– Covers losses occurring during the policy period – Regardless of when claim is “made” (reported)

• Claims-made policy
– Covers claims reported during policy period – Provided that the loss occurred after the “retroactive date” – “Tail” coverage

Business Income Insurance
• Also called “business interruption” insurance • Covers loss of “business income” and “extra expenses” that result from physical damage to covered property • “Business income”: pre-tax profit or loss that would have been earned, plus continuing normal operating expenses • “Extra expenses”: would not have been incurred without the loss – e.g., cost of temporary relocation, rent of substitute equipment

Commercial Multi-Peril (CMP)
• Also called “commercial package policy” (CPP) • Package policy: combination of two or more coverages into a single policy • Some advantages of a package policy:
– Convenience – Reduce potential gaps in protection – Don‟t need to deal with multiple insurers – a e.g., determining which insurer provides coverage in a given situation – Potentially lower premiums (vs. purchasing coverages separately)

Businessowners Policy
• Appropriate for small- to medium-sized businesses: stores, office buildings, apartment buildings

• Package policy
– Building

– Business personal property – Business income and extra expense – Business liability

Workers Compensation & Employers Liability (WC & EL)
• Part One: Workers compensation insurance
– Legal obligation for employers to provide benefits to injured (on-the-job) employees – Work-related injury or occupational disease – No “policy limit” – Statutory benefits per WC law in each state

• Part Two: Employers liability insurance
– For work-related injury/disease not compensated under state WC law

WC & EL (cont.)
• Some of the objectives of WC
– Sure, prompt, reasonable income -- regardless of fault – Single remedy  reduce delays and costs – Encourage employer interest in safety / rehabilitation

• Other issues:
– Who is an “employee”? – What constitutes “employment”?

Commercial Auto
• Liability coverage
– BI and PD – Accident caused by ownership / maintenance / use of covered auto

• Physical damage coverage • Numerical classifications and symbols

Professional Liability
• Medical malpractice
– Hospital and physicians & surgeons policies – Policy limits on per-incident and aggregate bases – Does not cover “general liability exposures”

• Errors and omissions
– Architects and engineers – Insurance agents and brokers

Boiler & Machinery
• Direct damage from covered cause of loss – e.g., explosions • Can also cover indirect loss (business income and extra expense) • Emphasis on loss prevention and safety
– Significant service / engineering activities

Ocean Marine
• Protection for goods transported over water • Significant history – e.g., Lloyd‟s of London • Classes of coverage:
– Hull – physical damage to ship – Cargo – covers shipper for damage or loss of goods – Protection and indemnity (P&I) – liability – Freight – covers ship owner for loss of earnings if goods damaged / lost

Inland Marine
• Protection for goods transported on land • Some classes of coverage:
– Domestic goods in transit
– Property held by bailees

– Mobile equipment and property – Means of transportation and communication

Title Insurance
• Protection against unknown defects in title • Characteristics:
– Protects against title defects that occurred prior to effective date of the policy – Insurer “assumes” that no losses will occur – Policy runs indefinitely – Single premium – Insured is indemnified in dollars (up to limit)

Commercial Umbrella
• Required underlying coverages
– E.g., CGL, business auto, EL

• Types of losses covered
– BI and PD – Personal and advertising injury

• Excess liability insurance
– Over underlying coverage, or – Over self-insured retention (SIR)

A Ratemaking Issue: Adverse Selection
• Examples
– – – – Flood plain Health and life insurance High-risk drivers Non-insurance: used cars (the “lemons problem”)

• Solution: underwriting; pricing

Risk Theory and Insurer Solvency

Risk Theory
• Typically, risk theory involves the mathematical specification of the evolution of an insurer‟s financial condition

E.g., U(t) = u + c t – S(t) • Annual aggregate losses are generally estimated by specifying two stochastic processes:
– Frequency (number of claims) – Severity (size of claim, given there is a claim)

A.M. Best’s Insolvency Study
• June, 1991 • Property / casualty insurers • 1969-1990 • 372 total insolvencies (302 for which a primary cause of insolvency could be determined)

Best’s Insolvency Study (cont.)
• Primary causes of insolvencies
– Deficient loss reserves 28%

– Rapid growth – Alleged fraud – Overstated assets
– Significant change in business

21 10 10

– Reinsurance failure – Catastrophe losses – Miscellaneous

7 6 9

Next Time
• Economics and the insurance market • References:
– Boor, 1998, “A Macroeconomic View of the Insurance Marketplace,” CAS Study Note

– Boor, 2004, “The Impact of the Insurance Economic Cycle on Insurance Pricing,” CAS Study Note

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