# On a dividend problem with random funding

## TL;DR

This paper extends the classical dividend maximization problem by incorporating random funding opportunities modeled via a Poisson process, providing explicit solutions for exponential claims and analyzing the impact of transaction costs.

## Contribution

It introduces a novel model combining dividend optimization with stochastic funding opportunities and derives explicit solutions for exponential claims.

## Key findings

- Explicit optimal strategy for exponential claims.
- Funding opportunities modeled via Poisson process.
- Impact of transaction costs on optimal strategy.

## Abstract

We consider a modification of the dividend maximization problem from ruin theory. Based on a classical risk process we maximize the difference of expected cumulated discounted dividends and total expected discounted additional funding (subject to some proportional transaction costs). For modelling dividends we use the common approach whereas for the funding opportunity we use the jump times of another independent Poisson process at which we choose an appropriate funding height. In case of exponentially distributed claims we are able to determine an explicit solution to the problem and derive an optimal strategy whose nature heavily depends on the size of the transaction costs.