Fair Premiums, Insurability of Risk and Contractual Provisions

1. Fair Premiums, Insurability of Risk and Contractual Provisions • Fair Insurance Premiums • What limit the insurability of risk • Contractual provisions • Legal Doctrines Ins301 Ch 8&10

2. Insurance Costs and Fair Premiums • Fair premium • The premium level that is just sufficient to fund the insurer’s expected costs and provide insurance company owners with a fair return on their investment. It includes • Expected claim costs • Investment income • Administrative costs • Fair profit loading Ins301 Ch 8&10

3. Claim tail and present value • The lag between the time that coverage is sold and claims are paid is known as the claim tail. • It affects expected losses Ins301 Ch 8&10

4. Example • Suppose a liability claim longs for 3 years. In the first year, the loss amount on average is $700. In the second year, the loss amount is $200. the loss amount is $100 in the third year. Interest rate is 5%. What is the expected loss? Ins301 Ch 8&10

5. Premium loadings • Two Bicycles one worth $200 and the other worth $6000. Assume that the probability of each bike being stolen is 0.05. Assume that the fixed costs of paying employees to market, underwrite, and process an application for bike insurance are $100 and that capital costs are 0. ignoring investment income, what are the fair premiums for both? Ins301 Ch 8&10

6. Moral Hazard • If you purchase a full-coverage theft insurance, will you still take precautions to reduce the likelihood of theft? Ins301 Ch 8&10

7. Conditions for Moral Hazard • Two conditions cause moral hazard • Expected losses depend on insured’s behavior • Effect of behavior on expected losses is costly to observe and measure • Example: • Claim costs increase with driving speed • Costly for insurers to monitor driving speed Ins301 Ch 8&10

8. Adverse Selection • If insurer is unable to distinguish between the two types of consumers with different risk level and thus change them the same premium, what will happen? Ins301 Ch 8&10

9. Factors Limiting the Insurability of Risk Ins301 Ch 8&10

10. Deductibles • Example: • policy with a $500 deductible • then policyholder pays first $500 of losses • Types of deductibles • per occurrence • aggregate Ins301 Ch 8&10

11. Deductibles and Claim Processing Costs • Deductibles reduce cost of processing small claims • Example: • Fixed claim processing cost of $200 $2000 with probability 0.01 Loss = 100 with probability 0.10 0 with probability 0.89 • Expected claim cost w/o a deductible = ______ • Expected claim cost w a $100 deductible = ______ • Marginal cost of insuring the $100 loss equals _______ Ins301 Ch 8&10

12. Deductibles, Moral Hazard, and Adverse Selection • Deductibles reduce moral hazard why? • Deductibles might be used to reduce adverse selection. How? Ins301 Ch 8&10

13. Coinsurance • With coinsurance, insured pays a proportion (the coinsurance rate) of any loss • Example: Insured pays 20% of all medical costs • Reason for coinsurance provisions • Insureds demand less than full insurance when the policy has a loading • Reduce moral hazard Ins301 Ch 8&10

14. Policy Limits • A policy limit is the maximum amount that the insurer will pay • Liability insurance always has a policy limit • Property insurance often has a policy limit Ins301 Ch 8&10

15. Purpose of Policy Limits • Reduce classification costs when consumers have information that is costly for insurers to obtain • Example: • Homeowners’ policy might limit coverage for jewelry losses to $2,500 • Those with more expensive jewelry buy special coverage • Insurer does not have to investigate the value of each policyholder’s jewelry Ins301 Ch 8&10

16. Pro Rata and Excess Coverage Clauses • Issue: How is coverage divided when multiple policies apply to the same loss • Pro rata clause: divide in proportion to amount of coverage • Excess clause: one policy pays losses in excess of the other policy’s limit • Why have these clauses? • prevent coverage in excess of loss, which would cause moral hazard Ins301 Ch 8&10

17. Exclusions • Policies exclude coverage for some types of losses • Why? • reduce administrative costs • reduce capital costs • reduce moral hazard • reduce adverse selection Ins301 Ch 8&10

18. Indemnity versus Valued Contracts • Indemnity contract - insurer pays based on the amount of loss that occurred • Example: auto physical damage • Valued contract - insurer pays a pre-determined amount • Example: life insurance Ins301 Ch 8&10

19. Indemnity versus Valued Contracts • Type of contract is largely explained by • The costs of assessing value: when the amount of loss can be assessed at low cost following the loss, more likely to have indemnity contracts • Moral hazard: when moral hazard is less likely to be a problem, fixing the insurance payment before a loss can avoid costly haggling following a loss (e.g., life insurance) Ins301 Ch 8&10

20. Insurance-to-Value in Property Insurance • Also called coinsurance • Specifies the percentage of the property’s value that must be insured to receive full reimbursement in the event of a loss • Typical coinsurance percentage is 80% Ins301 Ch 8&10

21. Legal Doctrines • Indemnity principle: an insurance policy cannot pay more than the financial loss suffered. • Insurable interest: if you want to get paid from insurance company, you got to have interest. • Example, A and B are not related, A buys a life insurance and set B as the beneficiary • Subrogation: after a party receives claim payment from an insurer, it has to transfer the right to seek additional compensation to the insurer Ins301 Ch 8&10

22. Legal Doctrines • Utmost good faith • Misrepresentation (page 195) • Concealment (196) • Contract of adhesion • Favors insureds, if disagreement • Doctrine of reasonable expectation • Policies would be interpreted based on the expectation of a person who is trained in the law. Ins301 Ch 8&10