TITLE:
Combined Optimal Stopping and Mixed Regular-Singular Control of Jump Diffusions
AUTHORS:
Charles Kusaya, Memory Mandiudza, Nicholas Mwareya, Confess Matete, Leonard Shambira, Nyashadzashe Ngaza
KEYWORDS:
Jump-Diffusion, Brownian Motion, Solvency Region, Optimal Stopping Time, Mixed Regular-Singular Control, Reinsurance
JOURNAL NAME:
Journal of Mathematical Finance,
Vol.11 No.2,
April
1,
2021
ABSTRACT: In this paper, we examine a model that
maximises dividend payments for an insurance company with a debt liability. We
assume that the company has a policy to reinvest a proportion of its surplus
cash before paying dividends to shareholders. We model the dynamics of the cash
reserves as a jump-diffusion process. Combined optimal stopping and mixed
regular-singular control of the jump-diffusion process is presented and
investigated. In the paper, we show that when the premium rateis less than the liability rate , then the company should not get into
business and the optimal dividend policy is to immediately pay out the initial
cash reserve as dividends to shareholders. For the case , we show that the optimal risk management
depends on the current level of the cash reserves. We demonstrate that the
company’s optimal dividend policy is to pay out as dividends surplus cash above
a predetermined threshold. We also present numerical examples to illustrate the
results obtained.