On the absolute ruin problem in a Sparre Andersen risk model with constant interest

Ilie-Radu Mitric, Andrei L. Badescu and David A. Stanford

Insurance: Mathematics and Economics, 2012, vol. 50, issue 1, 167-178

Abstract: In this paper, we extend the work of Mitric and Sendova (2010), which considered the absolute ruin problem in a risk model with debit and credit interest, to renewal and non-renewal structures. Our first results apply to MAP processes, which we later restrict to the Sparre Andersen renewal risk model with interclaim times that are generalized Erlang (n) distributed and claim amounts following a Matrix-Exponential (ME) distribution (see for e.g. Asmussen and O’Cinneide (1997)). Under this scenario, we present a general methodology to analyze the Gerber–Shiu discounted penalty function defined at absolute ruin, as a solution of high-order linear differential equations with non-constant coefficients. Closed-form solutions for some absolute ruin related quantities in the generalized Erlang (2) case complement the results obtained under the classical risk model by Mitric and Sendova (2010).

Keywords: Absolute ruin; Gerber–Shiu discounted penalty function; Markovian arrival process; Matrix-exponential distribution (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:50:y:2012:i:1:p:167-178

DOI: 10.1016/j.insmatheco.2011.10.009

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