Optimal investment and proportional reinsurance in a regime-switching market model under forward preferences

TL;DR

This paper develops a model for an insurance company's optimal investment and reinsurance strategies in a regime-switching market, using forward dynamic utility, and provides numerical analysis of the strategies' sensitivities.

Contribution

It introduces a novel framework combining forward utility with regime-switching models for optimal reinsurance and investment decisions.

Findings

Explicit characterization of optimal strategies

Construction of a forward utility function

Sensitivity analysis of model parameters

Abstract

In this paper we study the optimal investment and reinsurance problem of an insurance company whose investment preferences are described via a forward dynamic exponential utility in a regime-switching market model. Financial and actuarial frameworks are dependent since stock prices and insurance claims vary according to a common factor given by a continuous time finite state Markov chain. We construct the value function and we prove that it is a forward dynamic utility. Then, we characterize the investment strategy and the optimal proportional level of reinsurance. We also perform numerical experiments and provide sensitivity analyses with respect to some model parameters.