A Perturbation Approach to Optimal Investment, Liability Ratio, and Dividend Strategies

TL;DR

This paper develops a perturbation method to derive closed-form solutions for the optimal investment, liability ratio, and dividend strategies of an insurer aiming to maximize expected utility over an infinite horizon.

Contribution

It introduces a novel perturbation approach to solve a complex stochastic control problem with explicit solutions for log and power utility cases.

Findings

Optimal strategies depend on model parameters and risk aversion.

Closed-form solutions facilitate economic analysis.

Parameter variations significantly influence the insurer's decisions.

Abstract

We study an optimal dividend problem for an insurer who simultaneously controls investment weights in a financial market, liability ratio in the insurance business, and dividend payout rate. The insurer seeks an optimal strategy to maximize her expected utility of dividend payments over an infinite horizon. By applying a perturbation approach, we obtain the optimal strategy and the value function in closed form for log and power utility. We conduct an economic analysis to investigate the impact of various model parameters and risk aversion on the insurer's optimal strategy.