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On the absolute ruin in a MAP risk model with debit interest

Part of: Mathematical economics

Published online by Cambridge University Press:  01 July 2016

Zhimin Zhang ,
Hailiang Yang  and
Hu Yang
Zhimin Zhang*
Affiliation:
Chongqing University
Hailiang Yang*
Affiliation:
The University of Hong Kong
Hu Yang*
Affiliation:
Chongqing University
*
∗ Postal address: Department of Statistics and Actuarial Science, Chongqing University, Chongqing, P. R. China.
∗∗∗ Postal address: Department of Statistics and Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Kong.
∗ Postal address: Department of Statistics and Actuarial Science, Chongqing University, Chongqing, P. R. China.
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Abstract

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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.

Keywords

MAPabsolute ruindiscounted penalty functionmatrix renewal equationasymptoticheavy-tailed distribution

MSC classification

Primary: 91B30: Risk theory, insurance
Secondary: 91B70: Stochastic models
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 43 , Issue 1 , March 2011 , pp. 77 - 96
Copyright
Copyright © Applied Probability Trust 2011 

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