Finite-Horizon Ruin Probabilities in a Risk-Switching Sparre Andersen Model

Lesław Gajek () and Marcin Rudź ()
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Lesław Gajek: Institute of Mathematics Lodz University of Technology
Marcin Rudź: Institute of Mathematics Lodz University of Technology

Methodology and Computing in Applied Probability, 2020, vol. 22, issue 4, 1493-1506

Abstract: Abstract After implementation of Solvency II, insurance companies can use internal risk models. In this paper, we show how to calculate finite-horizon ruin probabilities and prove for them new upper and lower bounds in a risk-switching Sparre Andersen model. Due to its flexibility, the model can be helpful for calculating some regulatory capital requirements. The model generalizes several discrete time- as well as continuous time risk models. A Markov chain is used as a ‘switch’ changing the amount and/or respective wait time distributions of claims while the insurer can adapt the premiums in response. The envelopes of generalized moment generating functions are applied to bound insurer’s ruin probabilities.

Keywords: Risk operators; Risk-switching models; Ruin probabilities; Mgf’s envelopes; Risk management based on internal models; Solvency II; 91B30; 60J20; 60J22 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s11009-018-9627-2

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