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

Peng Li, Chuancun Yin, Ming Zhou

China Institute for Actuarial Science, Central University of Finance and Economics, Beijing, China.
School of Mathematical Sciences, Qufu Normal University, Qufu, China.

DOI: 10.4236/am.2014.513187                

Abstract

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.

Keywords

Hybrid Dividend Strategy, Compound Poisson Risk Model, Moment-Generating Function, Gerber-Shiu Function

Conflicts of Interest

The authors declare no conflicts of interest.

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