Optimal Insurance for a Prudent Decision-Maker Under Heterogeneous Beliefs

27 Pages Posted: 7 Dec 2021 Last revised: 19 Apr 2022

See all articles by Mario Ghossoub

Mario Ghossoub

University of Waterloo

Wenjun Jiang

University of Calgary

Jiandong Ren

University of Western Ontario

Date Written: April 17, 2022

Abstract

In this paper we extend some of the results in the literature on optimal insurance under heterogeneous beliefs in the presence of the no-sabotage condition, by allowing the likelihood ratio to be non-monotone. Under the assumption of prudence and a mild smoothness condition on the likelihood ratio, we first partition the whole domain of the underlying losses into disjoint regions and then obtain an explicit parametric form for the optimal indemnity function over each piece, by resorting to the marginal indemnity function formulation. The case where there exists belief singularity between the decision maker and the insurer is also studied. As an illustration, we consider a special case of our setting in which the premium principle is a distortion premium principle. We then obtain a closed-form characterization of the optimal indemnity for the cases where premia are determined by Value-at-Risk and Tail Value-at-Risk. Our study complements the literature and provides new insights into several similar problems.

Keywords: Optimal insurance, heterogeneous beliefs, no-sabotage condition, marginal indemnity function, likelihood ratio

JEL Classification: C70, G22

Suggested Citation

Ghossoub, Mario and Jiang, Wenjun and Ren, Jiandong, Optimal Insurance for a Prudent Decision-Maker Under Heterogeneous Beliefs (April 17, 2022). Available at SSRN: https://ssrn.com/abstract=3979051 or http://dx.doi.org/10.2139/ssrn.3979051

Mario Ghossoub (Contact Author)

University of Waterloo ( email )

Dept. of Statistics & Actuarial Science
200 University Ave. W.
Waterloo, Ontario N2L 3G1
Canada

HOME PAGE: http://uwaterloo.ca/scholar/mghossou

Wenjun Jiang

University of Calgary ( email )

612 Campus Place N.W.
University of Calgary
Calgary, Alberta T2N 1N4
Canada

Jiandong Ren

University of Western Ontario ( email )

1151 Richmond Street
Suite 2
London, Ontario N6A 5B8
Canada

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