Variance Contracts

42 Pages Posted: 27 Aug 2020

See all articles by Yichun Chi

Yichun Chi

Central University of Finance and Economics (CUFE)

Xun Yu Zhou

Columbia University - Department of Industrial Engineering and Operations Research (IEOR)

Sheng Chao Zhuang

University of Nebraska Lincoln

Date Written: July 12, 2020

Abstract

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.

Keywords: insurance design; expected value principle; variance; incentive compatibility; comparative statics

JEL Classification: G22, D81, D82

Suggested Citation

Chi, Yichun and Zhou, Xunyu and Zhuang, Sheng Chao, Variance Contracts (July 12, 2020). Available at SSRN: https://ssrn.com/abstract=3656850 or http://dx.doi.org/10.2139/ssrn.3656850

Yichun Chi

Central University of Finance and Economics (CUFE) ( email )

39 South College Road
Haidian District
Beijing, Beijing 100081
China

Xunyu Zhou

Columbia University - Department of Industrial Engineering and Operations Research (IEOR) ( email )

331 S.W. Mudd Building
500 West 120th Street
New York, NY 10027
United States

Sheng Chao Zhuang (Contact Author)

University of Nebraska Lincoln ( email )

Lincoln, NE 68588
United States
4024722330 (Phone)

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