TITLE:
Dividend Payments with a Hybrid Strategy in the Compound Poisson Risk Model
AUTHORS:
Peng Li, Chuancun Yin, Ming Zhou
KEYWORDS:
Hybrid Dividend Strategy, Compound Poisson Risk Model, Moment-Generating Function, Gerber-Shiu Function
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.13,
July
14,
2014
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.