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The Perturbed Compound Poisson Risk Process with Investment and Debit Interest

Chuancun Yin () and Chunwei Wang ()
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Chuancun Yin: Qufu Normal University
Chunwei Wang: Qufu Normal University

Methodology and Computing in Applied Probability, 2010, vol. 12, issue 3, 391-413

Abstract: Abstract In this paper, we study absolute ruin questions for the perturbed compound Poisson risk process with investment and debit interests by the expected discounted penalty function at absolute ruin, which provides a unified means of studying the joint distribution of the absolute ruin time, the surplus immediately prior to absolute ruin time and the deficit at absolute ruin time. We first consider the stochastic Dirichlet problem and from which we derive a system of integro-differential equations and the boundary conditions satisfied by the function. Second, we derive the integral equations and a defective renewal equation under some special cases, then based on the defective renewal equation we give two asymptotic results for the expected discounted penalty function when the initial surplus tends to infinity for the light-tailed claims and heavy-tailed claims, respectively. Finally, we investigate some explicit solutions and numerical results when claim sizes are exponentially distributed.

Keywords: Compound Poisson process; Absolute ruin; Expected discounted penalty function; Debit interest; Asymptotic; Defective renewal equations; Stochastic Dirichlet problem; Primary 91B30; Secondary 60K05, 91B70 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s11009-008-9109-z

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