Ida Lundmark: Optimization of Deductible Levels to Maximize Portfolio Utility in Insurance

Abstract.

This thesis investigates how an insurance company can determine optimal deductible levels using Borch’s theorem to maximize expected utility across a diverse portfolio, given an expected premium. Individual wealth characteristics, a key factor in Borch’s framework, are assigned to each policyholder. Assuming a Bernoulli utility function, we compare the impact of Gamma and compound Poisson loss distributions on a representative policyholder, ultimately selecting the compound Poisson for final analysis. Using this framework, optimal deductibles are then numerically calculated for each policyholder and clustered into two- and three-level deductible options. The study also examines how varying wealth levels affect these results and the application of Borch’s theorem.