Minimizing ruin probability under dependencies for insurance pricing

TL;DR

This paper investigates how dependencies between risks affect the optimal security loading in insurance pricing by analyzing ruin probabilities in various dependency scenarios.

Contribution

It introduces a comprehensive analysis of dependent risk structures and their impact on optimal insurance loadings, extending previous models that assumed independence.

Findings

Optimal loadings are independent of initial reserve in single-risk cases.

Dependencies influence optimal loadings in multiple-risk scenarios.

Loadings minimizing ruin probability differ from profit-maximizing loadings.

Abstract

In this work the ruin probability of the Lundberg risk process is used as a criterion for determining the optimal security loading of premia in the presence of price-sensitive demand for insurance. Both single and aggregated claim processes are considered and the independent and the dependent cases are analyzed. For the single-risk case, we show that the optimal loading does not depend on the initial reserve. In the multiple risk case we account for arbitrary dependency structures between different risks and for dependencies between the probabilities of a client acquiring policies for different risks. In this case, the optimal loadings depend on the initial reserve. In all cases the loadings minimizing the ruin probability do not coincide with the loadings maximizing the expected profit.