# Optimal Dividends in the Dual Risk Model under a Stochastic Interest Rate

## TL;DR

This paper investigates optimal dividend strategies in a dual risk model with stochastic interest rates, deriving closed-form solutions when the discount rate follows a geometric Brownian motion or exponential Lévy process.

## Contribution

It extends the dual risk model to include stochastic interest rates, providing the first closed-form solutions under these conditions.

## Key findings

- Closed-form solutions for optimal dividends with stochastic interest rates.
- Analysis under geometric Brownian motion and exponential Lévy processes.
- Enhances practical modeling of risk and discounting in finance.

## Abstract

Optimal dividend strategy in dual risk model is well studied in the literatures. But to the best of our knowledge, all the previous works assumes deterministic interest rate. In this paper, we study the optimal dividends strategy in dual risk model, under a stochastic interest rate, assuming the discounting factor follows a geometric Brownian motion or exponential L\'evy process. We will show that closed form solutions can be obtained.