Analysis of ruin measures for two classes of risk processes with stochastic income

Year 2015, Volume: 44 Issue: 4, 909 - 921, 01.08.2015

Wuyuan Jiang Chaoqun Ma

Abstract

In this paper, we consider the ruin measures for two classes of risk processes. We assume that the claim number processes are independent
Poisson and generalized Erlang(n) processes, respectively. Historically,
it has been assumed that the premium size is a constant. In this contribution, the premium income arrival process is a Poisson process. In
this framework, both the integro-differential equation and the Laplace
transform for the expected discounted penalty function are established.
Explicit expressions for the expected discounted penalty function are
derived when the claim amount distributions belong to the rational
family. Finally, numerical examples are considered. 

Keywords

Two classes of risk processes, Expected discounted penalty function, Integro-differential equation, Laplace transform, Stochastic income

References

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