Insurance With Heterogeneous Preferences

35 Pages Posted: 8 Oct 2020 Last revised: 5 Jul 2022

See all articles by Tim J. Boonen

Tim J. Boonen

University of Amsterdam

Fangda Liu

Georgia State University; University of Waterloo - Department of Statistics and Actuarial Science

Date Written: June 20, 2022


This paper studies an optimal insurance problem with finitely many potential policyholders. A monopolistic, risk-neutral insurer offers an insurance contract, and exponential utility maximizing individuals accept the offer or not. We allow for heterogeneity in the preferences of the individuals, while the insurer cannot discriminate in the insurance premium. We show that it is optimal for the insurer to offer only a full insurance contract, and the price optimization problem is reduced to a discrete problem, where the premium is an indifference premium for one individual in the market. Moreover, if individuals can self-select their insurance coverage given the market premium rate, then we find that partial insurance is generally optimal. Since the risk aversion parameters of individuals is generally unobserved, we also present a simulation-based framework. We show its convergence, and provide numerical examples.

Keywords: insurance contract theory, multiple policyholders, heterogeneous preferences, proportional insurance.

JEL Classification: D42,G22

Suggested Citation

Boonen, Tim J. and Liu, Fangda and Liu, Fangda, Insurance With Heterogeneous Preferences (June 20, 2022). Journal of Mathematical Economics, Forthcoming, Available at SSRN: or

Tim J. Boonen (Contact Author)

University of Amsterdam ( email )

Roetersstraat 11
Amsterdam, 1018 WB


Fangda Liu

University of Waterloo - Department of Statistics and Actuarial Science ( email )

Waterloo, Ontario N2L 3G1

Georgia State University ( email )

35 Broad St NW
Apt 1110
Atlanta, GA 30303
United States
4703789998 (Phone)

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