2020/08/17 by Yichun Chi, Xun Yu Zhou, Chi, Yichun +3
Business, Management and Accounting · Economics, Econometrics and Finance · Social Sciences · #FOS: Economics and business #Financial Literacy, Pension, Retirement Analysis #Insurance and Financial Risk Management #Insurance, Mortality, Demography, Risk Management #Risk Management (q-fin.RM)
paper · pdf · doi:10.48550/arxiv.2008.07103
openalex publication_date 2020/08/17 · openalex created_date 2024/04/10 · openalex updated_date 2026/07/28
We study the design of an optimal insurance contract in which the insured maximizes her expected utility and the insurer limits the variance of his risk exposure while maintaining the principle of indemnity and charging the premium according to the expected value principle. We derive the optimal policy semi-analytically, which is coinsurance above a deductible when the variance bound is binding. This policy automatically satisfies the incentive-compatible condition, which is crucial to rule out ex post moral hazard. We also find that the deductible is absent if and only if the contract pricing is actuarially fair. Focusing on the actuarially fair case, we carry out comparative statics on the effects of the insured's initial wealth and the variance bound on insurance demand. Our results indicate that the expected coverage is always larger for a wealthier insured, implying that the underlying insurance is a normal good, which supports certain recent empirical findings. Moreover, as the variance constraint tightens, the insured who is prudent cedes less losses, while the insurer is exposed to less tail risk.