151. Finite-horizon general insolvency risk measures in a regime-switching Sparre Andersen model
- Author
-
Lesław Gajek and Marcin Rudź
- Subjects
Statistics and Probability ,0209 industrial biotechnology ,Insolvency ,Markov chain ,business.industry ,General Mathematics ,Risk measure ,02 engineering and technology ,State (functional analysis) ,Function (mathematics) ,01 natural sciences ,Measure (mathematics) ,010104 statistics & probability ,020901 industrial engineering & automation ,Operator (computer programming) ,Applied mathematics ,0101 mathematics ,business ,Risk management ,Mathematics - 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.
- Published
- 2020