Open AccessFinite-Horizon Ruin Probabilities in a Risk-Switching Sparre Andersen Model
Author(s) -
Lesław Gajek,
Marcin Rudź
Publication year - 2018
Publication title -
methodology and computing in applied probability
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 32
eISSN - 1573-7713
pISSN - 1387-5841
DOI - 10.1007/s11009-018-9627-2
Subject(s) - ruin theory , mathematics , solvency , risk model , markov chain , flexibility (engineering) , mathematical economics , moment (physics) , discrete time and continuous time , time horizon , laplace transform , econometrics , capital requirement , actuarial science , mathematical optimization , statistics , economics , finance , mathematical analysis , physics , microeconomics , classical mechanics , market liquidity , incentive
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.