Revisiting Optimal Insurance Design Under Smooth Ambiguity Aversion

44 Pages Posted: 25 Jul 2022

See all articles by Yichun Chi

Yichun Chi

Central University of Finance and Economics (CUFE)

Richard Peter

University of Iowa

Wei Wei

University of Wisconsin - Milwaukee

Date Written: July 19, 2022

Abstract

We analyze optimal insurance design for a risk- and ambiguity-averse policyholder who is uncertain about the distribution of losses and faces linear transaction costs. We use smooth ambiguity preferences, a flexible ambiguity structure, and focus on indemnity schedules that satisfy the principle of indemnity and the no-sabotage condition for incentive compatibility. We characterize optimal insurance contracts and find that the marginal indemnity is either zero or one except at critical points. We then provide a condition for a straight deductible to be optimal and show that this condition is satisfied under various stochastic ordering assumptions on the priors. We discuss specific ambiguity structures, some of which give rise to indemnities with multiple layers. We also derive comparative statics. Greater ambiguity aversion always raises insurance demand whereas greater ambiguity has indeterminate effects. For policyholders with relative ambiguity prudence between zero and two, greater ambiguity raises insurance demand.

Keywords: insurance design, risk sharing, ambiguity, deductible, no-sabotage condition, comparative statics

JEL Classification: D81, D86, G22

Suggested Citation

Chi, Yichun and Peter, Richard and Wei, Wei, Revisiting Optimal Insurance Design Under Smooth Ambiguity Aversion (July 19, 2022). Available at SSRN: https://ssrn.com/abstract=4167175 or http://dx.doi.org/10.2139/ssrn.4167175

Yichun Chi

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

39 South College Road
Haidian District
Beijing, Beijing 100081
China

Richard Peter

University of Iowa ( email )

341 Schaeffer Hall
Iowa City, IA 52242-1097
United States

Wei Wei (Contact Author)

University of Wisconsin - Milwaukee ( email )

Bolton Hall 802
3210 N. Maryland Ave.
Milwaukee, WI 53211
United States

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