Dividend Payments with a Hybrid Strategy in the Compound Poisson Risk Model

• 作者: Chuancun Yin Ming Zhou Peng Li
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: HYBRID DIVIDEND STRATEGY Compound POISSON Risk Model Moment-Generating FUNCTION Gerber-Shiu FUNCTION
• 年，卷（期）: 2014,（13）
• 页码范围: 1933-1949
• 页数: 17页
• 分类号: O21

摘要

In this paper, a hybrid dividend strategy in the compound Poisson risk model is considered. In the absence of dividends, the surplus of an insurance company is modelled by a compound Poisson process. Dividends are paid at a constant rate whenever the modified surplus is in a interval;the premium income no longer goes into the surplus but is paid out as dividends whenever the modified surplus exceeds the upper bound of the interval, otherwise no dividends are paid. Integro-differential equations with boundary conditions satisfied by the expected total discounted dividends until ruin are derived;for example, closed-form solutions are given when claims are exponentially distributed. Accordingly, the moments and moment-generating functions of total discounted dividends until ruin are considered. Finally, the Gerber-Shiu function and Laplace transform of the ruin time are discussed.