On the Optimal Dividend Problem in the Dual Model with Surplus-Dependent Premiums

TL;DR

This paper investigates the optimal dividend distribution strategy in a dual risk model with surplus-dependent premiums, deriving conditions for optimality and providing numerical examples with exponential profit distributions.

Contribution

It introduces a framework for the dual risk model with surplus-dependent premiums and identifies conditions under which barrier strategies are optimal.

Findings

Derived the Hamilton-Jacobi-Bellman equation for the model

Established sufficient conditions for barrier strategy optimality

Provided numerical examples with exponential profit distribution

Abstract

This paper concerns the dual risk model, dual to the risk model for insurance applications, where premiums are surplus-dependent. In such a model premiums are regarded as costs, while claims refer to profits. We calculate the mean of the cumulative discounted dividends paid until ruin, if the barrier strategy is applied. We formulate associated Hamilton-Jacobi-Bellman equation and identify sufficient conditions for a barrier strategy to be optimal. Some numerical examples are provided when profits have exponential law.