Asymptotic results for perturbed risk processes with delayed claims

Insurance: Mathematics and Economics

Volumn 34, Issue 2, 2004, Pages 307-320

  Macci, Claudio ^a   Torrisi, Giovanni Luca ^b  

^a UNIVERSITY OF TURIN   (Italy)

^b CNR   (Italy)

Author keywords

Large deviations; Lundberg parameter; Perturbed risk process; Ruin probability; Shot noise

Indexed keywords

EID: 1842502047     PISSN: 01676687     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.insmatheco.2004.01.003     Document Type: Article

References (16)

1. Arjas E. The claims reserving problem in non-life insurance: some structural ideas Astin Bulletin 19 1989 139-152
2. Asmussen S. O'Cinneide C. On the tail of the waiting time in a Markov-modulated M/G/1 queue Operations Research 50 2002 559-565
3. Baldi P. Piccioni M. A representation formula for the large deviation rate function for the empirical law of a continuous time Markov chain Statistics and Probability Letters 41 1999 107-115
4. Brémaud, P., 1981. Point Processes and Queues. Martingale Dynamics. Springer-Verlag, New York.
5. Brémaud, P., 1999. Unpublished manuscript.
6. Brémaud P. An insensitivity property of Lundberg's estimate for delayed claims Journal of Applied Probability 37 2000 914-917
7. Dembo, A., Zeitouni, O., 1993. Large Deviations Techniques and Applications. Jones and Bartlett, Boston.
8. Duffield N.G. O'Connell N. Large deviations and overflow probabilities for a general single server queue, with applications Mathematical Proceedings of the Cambridge Philosophical Society 118 1995 363-374
9. Dufresne F. Gerber H.U. Risk theory for the compound Poisson process that is perturbed by diffusion Insurance: Mathematics and Economics 10 1991 51-59
10. Klüppelberg C. Mikosch T. Explosive Poisson shot noise processes with applications to risk reserves Bernoulli 1 1995 125 147
11. Macci C. Continuous-time Markov additive processes: composition of large deviations principles and comparison between exponential rates of convergences Journal of Applied Probability 38 2001 917-931
12. Neuhaus W. IBNR models with random delay distributions Scandinavian Actuarial Journal 1992 1992 97-107
13. Norberg R. Prediction of outstanding liabilities in non-life insurance Astin Bulletin 23 1993 95-115
14. Rolski, T., Schmidli, H., Schmidt, V., Teugels, J., 1999. Stochastic Processes for Insurance and Finance. Wiley, New York.
15. Schmidli H. Cramér-Lundberg approximations for ruin probabilities of risk processes perturbed by diffusion Insurance: Mathematics and Economics 16 1995 135-149
16. Waters H.R. Papatriandafylou A. Ruin probabilities allowing for delay in claims settlement Insurance: Mathematics and Economics 4 1985 113-122