Optimal Insurance to Minimize the Probability of Ruin: Inverse Survival Function Formulation

TL;DR

This paper develops a novel approach using inverse survival functions to determine optimal insurance contracts that minimize ruin probability, revealing deductible insurance with maximum limit as optimal under certain conditions.

Contribution

It introduces a new formulation of the insurance optimization problem using inverse survival functions, providing a solution for optimal deductible insurance with maximum limit.

Findings

Optimal insurance minimizes ruin probability under distortion premium principles.

Deductible insurance with maximum limit is identified as the optimal contract.

The inverse survival function approach simplifies the problem and yields explicit solutions.

Abstract

We find the optimal indemnity to minimize the probability of ruin when premium is calculated according to the distortion premium principle with a proportional risk load, and admissible indemnities are such that both the indemnity and retention are non-decreasing functions of the underlying loss. We reformulate the problem with the inverse survival function as the control variable and show that deductible insurance with maximum limit is optimal. Our main contribution is in solving this problem via the inverse survival function.