Math 479 / 568 Casualty Actuarial Mathematics

1. Math 479 / 568 Casualty Actuarial Mathematics Fall 2014 University of Illinois at Urbana-Champaign Professor Rick Gorvett Session 2: Risks and Risk Theory August 28, 2014

2. 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

3. 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

4. Vocabulary

5. 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

6. 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

7. 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

8. 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”

9. 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

10. 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

11. 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

12. Actuarial ScienceversusFinance

13. 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

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

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

16. Insurance Pure risk Loss or no loss No gain Law of large numbers More exposures ==> more accurate predictions Finance Speculative risk Loss or no loss or gain/profit Portfolio risk Diversification potential Insurance vs. FinanceRisk

17. InsurableRisks

18. 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

19. 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

20. Requirements of an Insurable Risk (cont.) • Calculable chance of loss • Frequency • Severity • Economically feasible premium • Affordable • Small relative to policy limit

21. Requirements of an Insurable Risk (cont.) • Which of the following are insurable risks? If not, why not? • War • Unemployment • Catastrophic meteor strike • Jobs re-training program

22. 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

23. Types of Insurance • Private • Life and health • Property-casualty • Lines of business • Reinsurance • Government • Social • Social security • Unemployment • Other • FDIC Fire Inland marine Ocean marine Personal auto Commercial auto Homeowners Commercial multi-peril Commercial liability Workers compensation ….

24. InsuranceandRisk Management

25. 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

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

27. Costs of Insurance to Society(the “dark side”) • Cost of doing business • Expenses • Fraud • Inflated claims

28. 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

29. 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

30. 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

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

32. 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

33. 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)

34. 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

35. Risk Management Techniques (cont.) Risk financing (cont.) • Non-insurance transfers • Contracts • Leases • Hold-harmless agreements • Insurance • Voluntary vs. mandatory • Deductibles • Excess insurance • Selection of insurer • Issues: • Price • Service • Solidity

36. Contract LawandInsurance Contracts

37. Requirements Of A Contract • Offer • Acceptance • Consideration • Legally competent parties • Legal purpose

38. 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

39. 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

40. 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

41. 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

42. 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

43. 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

44. 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

45. 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

46. Deductibles • 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)

47. Coinsurance • 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

48. Liability • 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

49. Elements of Negligence • A legalduty 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

50. 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