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March 2011 On the absolute ruin in a map risk model with debit interest
Zhimin Zhang, Hailiang Yang, Hu Yang
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Adv. in Appl. Probab. 43(1): 77-96 (March 2011). DOI: 10.1239/aap/1300198513

Abstract

In this paper we consider a risk model where claims arrive according to a Markovian arrival process (MAP). When the surplus becomes negative or the insurer is in deficit, the insurer could borrow money at a constant debit interest rate to repay the claims. We derive the integro-differential equations satisfied by the discounted penalty functions and discuss the solutions. A matrix renewal equation is obtained for the discounted penalty function provided that the initial surplus is nonnegative. Based on this matrix renewal equation, we present some asymptotic formulae for the discounted penalty functions when the claim size distributions are heavy tailed.

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Zhimin Zhang. Hailiang Yang. Hu Yang. "On the absolute ruin in a map risk model with debit interest." Adv. in Appl. Probab. 43 (1) 77 - 96, March 2011. https://doi.org/10.1239/aap/1300198513

Information

Published: March 2011
First available in Project Euclid: 15 March 2011

zbMATH: 1229.91171
MathSciNet: MR2761148
Digital Object Identifier: 10.1239/aap/1300198513

Subjects:
Primary: 91B30
Secondary: 91B70

Rights: Copyright © 2011 Applied Probability Trust

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Vol.43 • No. 1 • March 2011
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