Deficit distributions at ruin in a regime-switching Sparre Andersen model

Lesław Gajek
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  • Institute of Mathematics, Lodz University of Technology, Wólczańska 215, 90-924, Łódź, Poland
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and Marcin Rudź

Abstract

In this paper, we investigate deficit distributions at ruin in a regime-switching Sparre Andersen model. A Markov chain is assumed to switch the amount and/or respective wait time distributions of claims while the insurer can adjust the premiums in response. Special attention is paid to an operator 𝐋 generated by the risk process. We show that the deficit distributions at ruin during n periods, given the state of the Markov chain at time zero, form a vector of functions, which is the n-th iteration of 𝐋 on the vector of functions being identically equal to zero. Moreover, in the case of infinite horizon, the deficit distributions at ruin are shown to be a fixed point of 𝐋. Upper bounds for the vector of deficit distributions at ruin are also proven.

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JAA is devoted to applications of mathematical analysis, e.g. to economics, mathematical physics, mechanics and computer sciences. Topics include applications of mathematical analysis, differential equations, dynamical systems, optimization, optimal control, stochastic modeling and probability theory, numerical methods. The journal is jointly produced by the Institute of Mathematics of the Technical University of Lodz and De Gruyter.

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