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Finite-horizon general insolvency risk measures in a regime-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, 1507-1528

Abstract: Abstract Insolvency risk measures play important role in the theory and practice of risk management. In this paper, we provide a numerical procedure to compute vectors of their exact values and prove for them new upper and/or lower bounds which are shown to be attainable. More precisely, we investigate a general insolvency risk measure for a regime-switching Sparre Andersen model in which the distributions of claims and/or wait times are driven by a Markov chain. The measure is defined as an arbitrary increasing function of the conditional expected harm of the deficit at ruin, given the initial state of the Markov chain. A vector-valued operator L, generated by the regime-switching process, is introduced and investigated. We show a close connection between the iterations of L and the risk measure in a finite horizon. The approach assumed in the paper enables to treat in a unified way several discrete and continuous time risk models as well as a variety of important vector-valued insolvency risk measures.

Keywords: Vector-valued risk operators; Vector-valued loss measures at ruin; Risk management based on internal models; Markov chains; NWUE; Solvency II; 91B30; 60J20; 60J22 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s11009-020-09780-3

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