Optimal Insurance to Maximize RDEU Under a Distortion-Deviation Premium Principle

TL;DR

This paper investigates the optimal insurance design for risk-averse individuals aiming to maximize RDEU, considering a broad class of premium principles and ambiguity orders, with specific conditions for no insurance or deductible options.

Contribution

It introduces necessary and sufficient conditions for optimal insurance under a general distortion-deviation premium, extending previous models to include ambiguity considerations.

Findings

Optimal solutions characterized by necessary and sufficient conditions

Conditions under which no insurance or deductible insurance is optimal

Analysis of specific examples under various distortion-deviation premiums

Abstract

In this paper, we study an optimal insurance problem for a risk-averse individual who seeks to maximize the rank-dependent expected utility (RDEU) of her terminal wealth, and insurance is priced via a general distortion-deviation premium principle. We prove necessary and sufficient conditions satisfied by the optimal solution and consider three ambiguity orders to further determine the optimal indemnity. Finally, we analyze examples under three distortion-deviation premium principles to explore the specific conditions under which no insurance or deductible insurance is optimal.