Optimal Deductibles: A Theoretical Analysis from an Insured's Perspective

Abstract

A stop-loss policy as a tool for protection against a large loss is one of the most common insurance forms. For fixed premiums and therefore a uniquely determined insurance deductible, it has been well-established that the stop-loss form is superior to all other common insurance forms (Arrow, 1963). Using the expected premium principal, one can relax the assumption of a fixed premium and allow the insured to choose an arbitrary deductible that fits their needs. This thesis presents a stop-loss insurance policy model from an insured's perspective for a flexible premium. It shows the existence and uniqueness of an optimal deductible for a single risk model and derives several properties of the optimal deductibles in a bivariate excess-of-loss risk model where the insured faces two risks. The theoretical analysis is exemplied by several utility concepts which do not only illustrate the overall results but also give insights in the necessity of insurance and the influence of the risk structure on the findings.