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 rate is 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.
Highlights
Dividend decisions are mainly concerned with financial policies on the payment of cash dividends to shareholders in the present or at a latter date
We show that when the premium rate μ is less than the liability rate λ, 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
The results in this study have shown that there exists an optimal dividend policy for an insurance company that controls risk through proportional reinsurance, has a debt liability
Summary
Dividend decisions are mainly concerned with financial policies on the payment of cash dividends to shareholders in the present or at a latter date. Et al [10] present a dividend optimisation problem (for an insurer) with a jump-diffusion risk process in the presence of fixed and proportional transaction costs. The problem is solved under the risk-neutral assumption for the insurer and the value function together with the optimal policy is constructed. He and Liang [3] investigate optimal financing and dividend control of an insurance company with a proportional insurance policy. The underlying cash reserve dynamics is modelled using linear Brownian motion [3] considering an optimal dividend and reinsurance strategy of a property insurance company under catastrophe risk. Empirical studies have shown that the jump-diffusion process reflects better changes that can occur in the level of the liquid assets of an insur-
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