Optimizing expected utility of dividend payments for a Cram\'er-Lundberg risk proces

TL;DR

This paper addresses the problem of maximizing the discounted utility of dividend payments in an insurance company's Cramér-Lundberg risk process, deriving the optimal strategy under bounded dividend rates.

Contribution

It proves the value function satisfies the Hamilton-Jacobi-Bellman equation and explicitly identifies the optimal dividend strategy.

Findings

Optimal dividend strategy derived for Cramér-Lundberg process

Value function satisfies HJB equation

Optimal policy respects dividend rate constraints

Abstract

We consider the problem of maximizing the discounted utility of dividend payments of an insurance company whose reserves are modeled as a classical Cram\'er-Lundberg risk process. We investigate this optimization problem under the constraint that dividend rate is bounded. We prove that the value function fulfills the Hamilton-Jacobi-Bellman equation and we identify the optimal dividend strategy.