Optimal Insurance with Background Risk: An Analysis in the Presence of Moderate Negative Dependence

Abstract

As an individual or a corporation, there are various types of risks one faces. For many of these risks, there are insurance policies available for purchase that provide some protection against potential losses. However, there are also risks that are not insurable. These risks remain present as a background factor and affect the insured's final wealth. Consequentially, they have an impact on the optimal insurance for the insurable risk through the dependence structure between the insurable and uninsurable risk. In this thesis, we take a look at the optimal insurance problem given an insurable risk Xand a background risk Y that are partly moderately negative dependent. We will investigate the implications of this dependence structure for the optimal solution to the optimal insurance problem that uses an approach based on [Chi and Wei, 2018]. First, focusing on whether coverage is demanded or not, we later on make assumptions about the utility function of the insured and further specify the form of the dependence structure. These analytic results are followed up by a numerical analysis that has the goal to illustrate the previously obtained results of this thesis, and [Chi and Wei, 2018], for an exponentially distributed risk X, and a Pareto distributed risk X respectively.