Finite-Horizon Ruin Probabilities in a Risk-Switching Sparre Andersen Model
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.
KeywordsRisk operators Risk-switching models Ruin probabilities Mgf’s envelopes Risk management based on internal models Solvency II
Mathematics Subject Classification (2010)91B30 60J20 60J22
The authors thank the reviewers and the editors for helpful comments.
- Asmussen S (1989) Risk theory in a Markovian environment. Scand Actuar J 1989(2):66–100Google Scholar
- Gajek L, Rudź M (2013) Sharp approximations of ruin probabilities in the discrete time models. Scand Actuar J 2013(5):352–382Google Scholar
- Gajek L, Rudź M (2018) Banach Contraction Principle and ruin probabilities in regime-switching models. Insurance: Mathematics and Economics 80:45–53Google Scholar
- Solvency II (2009) Directive 2009/138/EC of the European Parliament and of the Council of 25 November 2009 on the taking-up and pursuit of the business of Insurance and Reinsurance (Solvency II). Official Journal of the European Union L 335/1, L 335/2, L 335/155Google Scholar
- Taylor GC (1976) Use of differential and integral inequalities to bound ruin and queuing probabilities. Scand Actuar J 1976(4):197–208Google Scholar
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