Asymptotic Analysis for Optimal Dividends in a Dual Risk Model

TL;DR

This paper investigates the asymptotic behavior of optimal dividend strategies in a dual risk model, providing insights into their performance when model parameters become very small or large.

Contribution

It offers the first asymptotic analysis of the optimal dividend problem in a dual risk model for extreme parameter values.

Findings

Asymptotic expressions for the value function in extreme parameter regimes

Insights into optimal dividend strategies under parameter limits

Guidance for practical implementation in high or low risk scenarios

Abstract

The dual risk model is a popular model in finance and insurance, which is often used to model the wealth process of a venture capital or high tech company. Optimal dividends have been extensively studied in the literature for a dual risk model. It is well known that the value function of this optimal control problem does not yield closed-form solutions except in some special cases. In this paper, we study the asymptotics of the optimal dividend problem when the parameters of the model go to either zero or infinity. Our results provide insights to the optimal strategies and the optimal values when the parameters are extreme.