A note on optimal expected utility of dividend payments with proportional reinsurance

TL;DR

This paper investigates the optimal dividend payout strategy for an insurance company using proportional reinsurance, maximizing expected utility with CRRA preferences, and analyzes the impact of initial reserves and parameters.

Contribution

It derives the optimal strategy by solving the Hamilton-Jacobi-Bellman equation and explores the asymptotic behavior of the value function for large reserves.

Findings

Optimal dividend and reinsurance strategies identified.

Asymptotic behavior of the value function analyzed.

Numerical examples demonstrate parameter sensitivity.

Abstract

In this paper, we consider the problem of maximizing the expected discounted utility of dividend payments for an insurance company that controls risk exposure by purchasing proportional reinsurance. We assume the preference of the insurer is of CRRA form. By solving the corresponding Hamilton-Jacobi-Bellman equation, we identify the value function and the corresponding optimal strategy. We also analyze the asymptotic behavior of the value function for large initial reserves. Finally, we provide some numerical examples to illustrate the results and analyze the sensitivity of the parameters.