Applied Mathematics

Volume 5, Issue 13 (July 2014)

ISSN Print: 2152-7385   ISSN Online: 2152-7393

Google-based Impact Factor: 0.58  Citations  

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

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DOI: 10.4236/am.2014.513187    3,149 Downloads   4,331 Views  Citations

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.

Share and Cite:

Li, P. , Yin, C. and Zhou, M. (2014) Dividend Payments with a Hybrid Strategy in the Compound Poisson Risk Model. Applied Mathematics, 5, 1933-1949. doi: 10.4236/am.2014.513187.

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