Optimal proportional reinsurance and investment for stochastic factor models

TL;DR

This paper develops an advanced stochastic control model for insurance companies to optimize reinsurance and investment strategies considering a stochastic factor affecting claim intensity, with solutions derived via PDEs and validated through numerical simulations.

Contribution

It introduces a stochastic factor into the classical model, derives optimal strategies using HJB equations, and proposes a new premium calculation rule for more realistic modeling.

Findings

Optimal strategies characterized via backward PDEs.

Existence and uniqueness of solutions established.

Numerical simulations demonstrate sensitivity and effectiveness.

Abstract

In this work we investigate the optimal proportional reinsurance-investment strategy of an insurance company which wishes to maximize the expected exponential utility of its terminal wealth in a finite time horizon. Our goal is to extend the classical Cramer-Lundberg model introducing a stochastic factor which affects the intensity of the claims arrival process, described by a Cox process, as well as the insurance and reinsurance premia. Using the classical stochastic control approach based on the Hamilton-Jacobi-Bellman equation we characterize the optimal strategy and provide a verification result for the value function via classical solutions of two backward partial differential equations. Existence and uniqueness of these solutions are discussed. Results under various premium calculation principles are illustrated and a new premium calculation rule is proposed in order to get more realistic strategies and to better fit our stochastic factor model. Finally, numerical simulations are performed to obtain sensitivity analyses.