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A class of risk processes with delayed claims: ruin probability estimates under heavy tail conditions

Part of: Mathematical economics Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Ayalvadi Ganesh  and
Giovanni Luca Torrisi
Ayalvadi Ganesh*
Affiliation:
Microsoft Research
Giovanni Luca Torrisi*
Affiliation:
Istituto per le Applicazioni del Calcolo, Roma
*
∗Postal address: Microsoft Research, 7 J J Thomson Avenue, Cambridge CB3 0FB, UK. Email address: [email protected]
∗∗Postal address: Istituto per le Applicazioni del Calcolo ‘M. Picone’ (IAC-CNR), Viale del Policlinico 137, 00161 Roma, Italia. Email address: [email protected]
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Abstract

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We consider a class of risk processes with delayed claims, and we provide ruin probability estimates under heavy tail conditions on the claim size distribution.

Keywords

Extreme value theoryPoisson processregular variationrenewal processruin probabilityshot noise processsubexponential distribution

MSC classification

Primary: 91B30: Risk theory, insurance 60G55: Point processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 43 , Issue 4 , December 2006 , pp. 916 - 926
Copyright
© Applied Probability Trust 2006 

References

Albrecher, H. and Asmussen, S. (2006). Ruin probabilities and aggregate claims distributions for shot noise Cox processes. Scand. Actuarial J. 2006, 86–110.Google Scholar
Albrecher, H. and Teugels, J. L. (2006). Exponential behavior in the presence of dependence in risk theory. J. Appl. Prob. 43, 257–273.Google Scholar
Asmussen, S. (2000). Ruin Probabilities. World Scientific, Singapore.Google Scholar
Asmussen, S. and Klüppelberg, C. (1996). Large deviations results for subexponential tails, with applications to insurance risk. Stoch. Process. Appl. 64, 103–125.Google Scholar
Asmussen, S., Schmidli, H. and Schmidt, V. (1999). Tail probabilities for non-standard risk and queueing processes with subexponential Jumps. Adv. Appl. Prob. 31, 422–447.CrossRefGoogle Scholar
Brémaud, P. (2000). An insensitivity property of Lundberg's estimate for delayed claims. J. Appl. Prob. 37, 914–917.Google Scholar
Embrechts, P. and Veraverbeke, N. (1982). Estimates for the probability of ruin with special emphasis on the possibility of large claims. Insurance Math. Econom. 1, 55–72.Google Scholar
Embrechts, P., Klüppelberg, C. and Mikosch, T. (1997). Modelling Extremal Events for Insurance and Finance. Springer, Berlin.Google Scholar
Goldie, C. M. and Resnick, S. (1988). Distributions that are both subexponential and in the domain of attraction of an extreme-value distribution. Adv. Appl. Prob. 20, 706–718.Google Scholar
Klüppelberg, C. and Mikosch, T. (1995a). Delay in claim settlement and ruin probability approximations. Scand. Actuarial J. 1995, 154–168.Google Scholar
Klüppelberg, C. and Mikosch, T. (1995b). Explosive Poisson shot noise processes with applications to risk reserves. Bernoulli 1, 125–147.Google Scholar
Klüppelberg, C., Mikosch, T. and Schärf, A. (2003). Regular variation in the mean and stable limits for Poisson shot noise. Bernoulli 9, 467–496.Google Scholar
Macci, C., Stabile, G. and Torrisi, G. L. (2005). Lundberg parameters for non standard risk processes. Scand. Actuarial J. 2005, 417–432.Google Scholar
Mikosch, T. and Nagaev, V. (1998). Large deviations of heavy-tailed sums with applications in insurance. Extremes 1, 81–110.Google Scholar
Rolski, T., Schmidli, H., Schmidt, V. and Teugels, J. L. (1999). Stochastic Processes for Insurance and Finance. John Wiley, Chichester.Google Scholar
Teugels, J. L. and Veraverbeke, N. (1973). Cramér-type estimates for the probability of ruin. CORE Discussion Paper 7316, Université catholique de Louvain.Google Scholar
Veraverbeke, N. (1977). Asymptotic behaviour of Wiener–Hopf factors of a random walk. Stoch. Process. Appl. 5, 27–37.CrossRefGoogle Scholar
Waters, H. R. and Papatriandafylou, A. (1985). Ruin probabilities allowing for delay in claims settlement. Insurance Math. Econom. 4, 113–122.Google Scholar
Yuen, K. C., Guo, J. and Ng, K. W. (2005). On ultimate ruin in a delayed-claims risk model. J. Appl. Prob. 42, 163–174.CrossRefGoogle Scholar