Ins301 Ch 8&10 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.