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Risk Management and Insurance: Perspectives in a Global Economy 19. The Economic Foundations of Insurance Click Here to Add Professor and Course Information There are two sections (Insurance Legal Principles; Insurance Contract Structure). Both are derived from Appendix Chapter 2. There are two sections (Insurance Legal Principles; Insurance Contract Structure). Both are derived from Appendix Chapter 2.

Study Points  Expected utility and the demand for insurance  Insurance supply: characteristics of ideal insurable exposures 3

Expected Utility and the Demand for Insurance 4

Recall the Cases  John and Mary Risk-averse utility function  XYZ Insurance Expected value theory Premium at cost 5

How Premium Is Calculated?  Cost  expected loss  Loadings for Internal expenses (e.g., underwriting and marketing) External fees (e.g., premium taxes and license fees)  Profits 6

Moral Hazard  The propensity of individuals to alter their behavior when risk is transferred to a third party, such as being less careful in: Maintaining health condition Driving House maintenance  Fraud as an extreme case 7

Insurance Demand in Markets with Moral Hazard  Ex-ante moral hazard Insurance fraud  Ex-post moral hazard  Insurer responses to moral hazard Controlling the marginal benefit of being careful or the marginal cost of being careless Loss sharing through deductible and coinsurance Insight 19.2 Rewarding insureds who undertake loss preventing activities Retrospective or experience rating 8 Discussion in page 482

Moral Hazard and Insurance Demand Andrew  Andrew, risk-averse salesperson Has €12,000 in cash and a car worth €4,000 Probability of accident depending on his driving behavior If not careful, p = 0.5 If careful, p = 0.2 but incurs additional expense of €1,000 Has a square root function for his wealth utility 9

Moral Hazard and Insurance Demand Ecu Insurance  Ecu Insurance Company Full insurance at the actuarially fair premium Should it consider Andrew is a safe or risky driver? If a safe driver: premium = 0.2 x €4,000 = €800 Otherwise: premium = 0.5 x €4,000 = €2,000 10

Insurer Responses to Moral Hazard  Controlling the marginal benefit of being careful or the marginal cost of being careless  Loss sharing through deductible and coinsurance Insight 19.2  Rewarding insureds who undertake loss preventing activities Retrospective or experience rating 11

Deductible and Coinsurance (Insight 19.2) 12 Deductible Coinsurance Deductible Stop loss Insurer’s Share Insured’s Share

Deductible and Coinsurance (Another Look) 13 Frequency Severity Deductible Coverage Limit Amount Retained Amount Financed Stop Loss Coinsurance

Insurance Demand in Markets with Adverse Selection  The effect of adverse selection on insurance markets  Insurer responses Eliciting more information about applicants and insureds Designing insurance contracts that encourage insureds with differing risk types to self-select into the most appropriate risk class Table Discussion in page

Adverse Selection and Insurance Demand Individual Rating  Two Japanese Risk averse and each with initial wealth of ¥125,000 Will suffer a ¥100,000 loss if cancer develops One is “low risk” (p = 0.25) and the other is “high risk” (p = 0.75) Insurance at actuarially fair premium 15

Adverse Selection and Insurance Demand Pooled Rating  If the insurer pools both risks Fair pooled premium [(¥75,000 + ¥25,000) ÷ 2] = ¥50,000 16

A Solution  Eliciting more information about applicants and insureds  Designing insurance contracts that encourage insureds with differing risk types to self-select into the most appropriate risk class 17

An Example Using a Simple Pricing Technique 18

Insurer’s Tool – Underwriting  Case A city with one health insurer, Monopoly Insurance All citizens must purchase health insurance. There are 1,000 good risk citizens and 1,000 bad risk citizens.  Will the insurer classify them into high and low risk classes and charge different premiums? No. Instead, it can treat all risks equal and charge the same premium. No medical exam would be required. 19

Insurer’s Tool – Underwriting  Suppose A good risk costs the insurer $1000 a year. A bad risk costs the insurer $5,000 a year.  The pooled premium is then: 20

Insurer’s Tool – Underwriting  Suppose now Competition Insurance enters the market. It has the risk information of the city. It wants to generate profits with minimum effort. Possible?  The result Monopoly Insurance goes out of business. 21 Medical Exam Required Those Who Pass Gets the Coverage for $2,000 of yearly premium. Those Who Fail Gets the Coverage for $4,000 of yearly premium.

Substitutes for Insurance  Substitutes Higher insurance prices tend to decrease the amount of market insurance purchased by risk-averse individuals and increase the amount of loss reduction “bought.”  Complements Loss prevention and market insurance are complements, not substitutes. An investment in loss prevention may actually raise the amount of risk that a risk-averse person faces and therefore raises the demand for market insurance. 22

Why Corporations Purchase Insurance 23

Why Corporations Purchase Insurance  Already covered are: Managerial self-interest Corporate taxation Cost of financial distress Capital market imperfections  Other reasons include: Insurers may offer real service efficiencies. Regulated industries have a higher demand for insurance. The purchase of some types of insurance is required by government. 24 Discussion continues from Chapter 2

“Ideal” Insurable Exposures – Not Necessarily Practical in Some Aspects 25

“Ideal” Insurable Exposures 1.Presence of numerous independent and identically distributed (IID) units 2.Unintentional losses 3.Easily determinable losses as to time, amount, and type 4.Economically feasible premium 26

Numerous IID Exposure Units  Each exposure unit (e.g., liability risk) in an insurance pool should be IID.  Two random variables (e.g., exposures units) are independent if the occurrence of an event affecting one of the variables has no affect on the other variable. The independence property is important because it affects how well insurers can diversify the systematic risk of their insurance pools.  Random variables are identically distributed if the probability distributions of two random variables prescribe the same probability to each potential occurrence. 27

Numerous IID Exposure Units  The law of large numbers Variance and standard deviation as measures of dispersion  Effects of pooling IID exposures units – A fire insurer would be interested in the following four statistics: The total amount of losses expected to be paid during the year; The standard deviation of the total loss distribution (to understand the riskiness inherent in providing this insurance) The average loss (to determine the premium to be charged); The standard deviation of the average loss distribution (to determine the risk each exposure unit contributes to the risk class) 28

Average Loss Distribution of an Insurance Pool (Figure 19.2) 29

Probability of Ruin (Figure 19.3) 30

Accidental Losses  Losses should be accidental or unintentional We made this point earlier in the context of moral hazard From a societal viewpoint, it clearly is not good public policy to allow policyholders to collect insurance proceeds for internationally causing losses.  Some losses occur naturally over time. It is usually less expensive to budget for possible repair or replacement of the property than to purchase insurance. 31

Determinable Losses  The details of the insured loss – time, place, and amount – must be verified and the payment amount agreed upon by the insured and the insurer.  The costs of verifying loss details should be relatively low for insurance to be offered at an economically feasible premium. 32

Economically Feasible Premiums  On the one hand, rational risk-averse individuals will pay a maximum premium equal to the expected value of the loss plus the risk premium. On the other, the owners of private insurance companies require that insurance rates be enough to give them a competitive return on their investments.  Factors affecting this range Competition in the market Threats of new entrances Price Threat of alternative products and substitutes The bargaining power of consumers The degrees of risk attitudes of consumers 33

Legal Aspects: A Short Visit Appendix Chapter A2 34

Legal Principles 1.Indemnity 2.Insurable interest 3.Utmost good faith 35

Indemnity  In nonlife insurance Actual cash value (ACV) Replacement cost Valued policy Other insurance provision Primary and excess insurance  Figure A2-1 Subrogation 36

Another Example of Primary and Excess 37 Personal Umbrella Liability Insurance (Liability Coverage) $1,000,000 Homeowner’s (Liability Coverage) $500,000 Personal Automobile (Liability Coverage) $300,000 Primary Excess

Indemnity  In life insurance No application of “other insurance” provision When applied, it could be in relation to the total earnings power of the insured life and the sum of life insurance in the aggregate of all outstanding policies Thus, life insurance policies are “valued policies.”  In health insurance ‘Coordination of benefits” 38

Insurable Interest  The principle: An insured must have a financial interest in the loss event that is the subject of the insurance contract for the policy.  Application in Nonlife insurance Bailment Life insurance Insurable interest for domestic partners  Insight A2-2 Viatical Settlements (and Death Bonds)  Insight A Bailment – Temporary change in possession of property but with no change in ownership

Utmost Good Faith  A higher degree of honesty on the parties to an insurance contract than what is expected from parties to other [legal] contracts  Information asymmetry problem inherent with insurance contracts

Utmost Good Faith – Applications  Misrepresentation Material response incorrectly made by an applicant in procuring insurance  Concealment Intentional failure to disclose material information  Warranty Statement of fact or promise that must be true for the insurer to be liable under the insurance contract 41

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Insurance Contract: A Short Visit Appendix Chapter A2 43

Characteristics  Aleatory contract The values exchanged by the contracting parties may not seem equal.  Unilateral contract Only one party (the insurer) has a legal duty to act.  Conditional contract The insurer is obligated to honor its promises only if the insured has complied with certain conditions specified in the policy. 44

Characteristics (continued)  Personal contract The agreement is between the insurer and the insured person (not the insured property). Hence, property insurance contracts cannot be assigned to another insured person without the insurer’s consent.  Contract of adhesion The contract is designed by one party and offered to another party on a "take it or leave it" basis.  Reasonable expectations doctrine It considers the objectively reasonable expectations of insureds and beneficiaries regarding the terms of insurance contracts. 45

The Insurance Contracting Process  Offer and acceptance Binding authority Conditional premium receipt  Consideration Insurer – promise to pay the stipulated insurance benefits Insured – complete application and initial premium payment  Legal competence Age?  Legal purpose 46

Structure of the Insurance Contract 1.Declarations 2.Insuring agreements 3.Exclusions 4.Conditions 5.Endorsements (riders) 47

Declarations (Page)  Policy limits Aggregate limits Sublimits such as: Per person limit Per occurrence limit  Loss sharing Deductible Elimination period (e.g., health insurance) Coinsurance 48 Insight A2-4 Automobile Liability Insurance Limits

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Insuring Agreements  Describes the nature of the insurer's obligations: Promises to pay certain sums upon the occurrence of enumerated events, for example: Property damage to covered property caused by insured perils Payment for settlements and judgments when the insured is found legally liable for activities covered in the contract Plus a duty to defend the insured against all allegations Life insurer’s promise to pay the beneficiary (or insured) certain amounts upon the death (or survival) of the insured In health insurance, reimbursement of covered medical expenses or the periodic payment of income for covered disabilities 50

Exclusions  A necessary element of the contract for the following reasons Insurable risks should be independent and identically distributed loss events. Problems of moral hazard must be addressed. When applicable, the insurer avoids overlapping coverage and the inefficiency created by such redundancy. Exclusions can serve to limit coverage to make the premium more affordable. 51

Conditions  The insured must meet these conditions to keep the policy valid and to receive applicable benefits. Prompt notification of a loss event Mitigation of the property from further loss Documentation of evidence Cooperation to the insurer and investigation 52

Conditions – Termination of Contract  Cancellation  Nonrenewal 53 Cancellation differs from voiding (avoiding) a contract or void contract.

Endorsements and Riders  Added to the standardized contract to modify the terms and conditions of the policy. Endorsements commonly used in nonlife insurance business Riders commonly in life insurance business 54

Discussion Questions 55

Discussion Question 1  Hannah owns a home worth US$50,000, which is subject to the risk of fire. The probability of a fire is 25 percent and the amount of damage due to the fire would be US$40,000. Assume Hannah’s utility function is the square root of wealth. Hannah has been offered full insurance at a cost of US$13,000. Will she buy the insurance? Why or why not? 56

Discussion Question 2  A frequency distribution shows the number of accidents that an insurer can expect from each exposure unit in its insurance pool during the year. Use the information provided below to answer the following questions: Calculate the expected number of accidents a single exposure unit could expect during the next year. Calculate the standard deviation of the number of accidents a single exposure unit could expect during the next year. Calculate the standard deviation of the number of accidents. 57

Discussion Question 3  Consider the following lotteries, x, y and z: Calculate the expected value of each gamble. Assuming a risk-averter’s utility function of wealth is given below. Calculate the expected utility of each gamble for a person who has an initial wealth level of 10. Which gamble does this person prefer? Why? 58