Optimal financing and dividend distribution in a general diffusion model with regime switching

TL;DR

This paper analyzes an optimal control problem for a surplus process modeled by a diffusion with regime switching, focusing on optimal dividend payouts and capital injections to maximize discounted dividends minus costs.

Contribution

It introduces a regime-switching diffusion model with restricted dividend rates and derives optimal policies for capital injections and dividend payments.

Findings

Optimal to inject capital only when surplus is below zero.

Dividends are paid at maximal rate when surplus exceeds a regime-dependent threshold.

The model accounts for regime-dependent drift and volatility functions.

Abstract

We study the optimal financing and dividend distribution problem with restricted dividend rates in a diffusion type surplus model where the drift and volatility coefficients are general functions of the level of surplus and the external environment regime. The environment regime is modeled by a Markov process. Both capital injections and dividend payments incur expenses. The objective is to maximize the expectation of the total discounted dividends minus the total cost of capital injections. We prove that it is optimal to inject capitals only when the surplus tends to fall below zero and to pay out dividends at the maximal rate when the surplus is at or above the threshold dependent on the environment regime.