On the expected discounted penalty function for a risk model with two classes of claims and random incomes

Year 2015, Volume: 44 Issue: 2, 485 - 501, 01.04.2015

Jie-hua Xie Wei Zou

https://izlik.org/JA66XC28YU

Abstract

In this paper, we consider a risk model with two independent classes
of insurance risks and random incomes. We assume that the two independent claim counting processes are, respectively, the Poisson and the
Erlang(2) process. When the individual premium sizes are exponentially distributed, the explicit expressions for the Laplace transforms
of the expected discounted penalty functions are derived. We prove
that the expected discounted penalty functions satisfy some defective
renewal equations. By employing an associated compound geometric
distribution, the analytic expressions for the solutions of the defective
renewal equations are obtained. Assuming that the distributions of premium sizes have rational Laplace transforms, we also give the explicit
representations for the Laplace transforms of the expected discounted
penalty functions.

Keywords

Compound Poisson risk model , Erlang risk process , Expected discounted penalty function , Random income

References

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