Modul IV

• Risk-averse insured with utility function u and initial wealth W

• Insured can either reduce loss size L(e) or probability of loss p(e) by effort e

• Wealth in no-loss state: YI=W-e, and in the loss state: YII:W-e-L

The insured maximizes expected utility by choosing effort e, given by: max E(u(Y))=(1-p(e))u(W-e)+p(e)u(W-e-L). Effort is optimal if it sufficiently reduces the loss probability.

Moral hazard occurs when insured individuals reduce their effort to prevent losses because the insurance shields them from the full financial consequences of the loss.

• ex-ante moral hazard: Behavior before the loss event, reducing the probability of a claim (e.g., risk mitigation efforts)

• ex-post moral hazard: Behavior after the loss, influencing claim size (e.g., overstating damages)

• The insured should only take partial insurance and should substitue coverage by investing in loss prevention

• Only second best option can be achived -> its not only a risk allocation but also providing incentives for the insured

• RAND Health Insurance Experiment: Found that more cost-sharing reduced medical visits but did not impact life expectancy (except for the poorest).

• Oregon Medicaid Experiment: Increasing insurance led to more medical visits, but both necessary and unnecessary care increased.

It denotes insured-induced changes in insureds behavior which occours if the insurer cannot separatly observe the insureds behavior and the exegenous risk

• If a insurance company has to cover a repair service, they have to distinguish between the price nad qunatity component

• The insured looses their importance for prices

• < 0 -> e is reduced more than linearly increasing coverage

• = 0 -> e is reduced linearly with increasing coverage

• > 0 -> e is reduced less than linearly increasing coverage