Abstract
In this paper, we study an optimal insurance problem, which allows the insured and the insurer to have heterogeneous probability beliefs in the distribution of potential losses, on the basis of which we maximize the expected utility of the insured’s final wealth. In order to reduce ex-post moral hazard, we assume that the alternative insurance contract follows the principle of indemnity and incentive compatibility constraints. Under the assumption of Wang’s premium principle, we derive a necessary and sufficient condition for the optimal solution. Then we discuss some particular characteristics of the optimal solution and the optimality of no insurance and full insurance.
Highlights
The research on insurance began in 1960s
We introduce an optimal insurance model with heterogeneous belief, in which the insurance contract satisfies the principle of indemnity and incentive compatibility constraints, and prove the existence and uniqueness of the optimal solution
Does not satisfy the additivity under Wang’s premium principle, so even if Q is absolutely continuous with respect to P, we cannot derive the uniqueness of the optimal solution
Summary
The research on insurance began in 1960s. Since the seminal work of (Arrow, 1963), the optimal insurance strategy has aroused great interest in research and practice, and has laid significant foundation in insurance economics. (Arrow, 1963) first studied this issue from the perspective of the insured, who seeks to maximize the expected utility of the final wealth. It should be noted that in these studies, both parties of the insurance contract have the same probability belief on potential loss distribution. The author proved that the optimal insurance contract with nonnegative indemnity constraint can have any form of expression through heuristic analysis, and introduced a very special form of belief heterogeneity This particularity is mainly reflected in the case of non-zero loss, both parties of the contract have the same conditional distribution, and the probability quality of zero loss of the insured is less than that of the insurer. We introduce an optimal insurance model with heterogeneous belief, in which the insurance contract satisfies the principle of indemnity and incentive compatibility constraints, and prove the existence and uniqueness of the optimal solution. Does not satisfy the additivity under Wang’s premium principle, so even if Q is absolutely continuous with respect to P, we cannot derive the uniqueness of the optimal solution
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