Simulating ruin probabilities for a class of semimartingales by importance sampling methods

Scandinavian Actuarial Journal

Volumn 2003, Issue 3, 2003, Pages 178-216

  Paulsen, Jostein ^a   Rasmussen, Bo Normann ^a  

^a UNIVERSITY OF BERGEN   (Norway)

Author keywords

Extreme value distribution; Girsanov's theorem; Importance sampling; Jump diffusion process; L vy process; Monte carlo simulation; Ruin probability; Semimartingale

Indexed keywords

EID: 85011210599     PISSN: 03461238     EISSN: 16512030     Source Type: Journal    
DOI: 10.1080/03461230110106354     Document Type: Article

References (29)

1. Asmussen, S. (1985). Conjugate processes and the simulation of ruin problems. Stochastic Processes and their Applications 20, 213-229.
2. Asmussen, S. (1999) Stochastic simulation with a view towards stochastic processes. MaPhySto Lecture Notes, University of Aarhus 2.
3. Asmussen, S. & Binswanger, K. (1997). Simulation of ruin probabilities for subexponential claims. AUSTIN Bulletin 27, 297-318.
4. Asmussen, S. & Nielsen, H. M. (1995). Ruin probabilities via local adjustment coefficients. Journal of Applied Probability 32, 736-755.
5. Asmussen, S. & Rubinstein, R. Y. (1995). Complexity properties of steady state reare events simulation in queueing models. In: Dshalalow, J. (ed.). Frontiers queuing. CRC Press, Boca Raton.
6. Barndorff-Nielsen, O. E. (1997). Normal inverse Gaussian distributions and stochastic volatility modelling. Scandinavian Journal of Statistics 24, 1-14.
7. Dufresne, F. & Gerber, H. U. (1991). Risk theory for the compound Poisson process that is perturbed by diffusion. Insurance: Mathematics and Economics 10, 51- 59.
8. Embrechts, P., KKppelberg, C. & Mikosch, T. (1997). Modeling extremely events. Springer, Berlin, Heidelberg.
9. Geary, R. C. (1935). The ratio of the mean deviation to the standard deviation as a test of normality. Biometrika 27, 310-332.
10. Heidelberger, P. (1995). Fast simulation of rare events in queueing and reliability theory. ACM Transactions on Computer Modelling and Simulation 5, 43-85.
11. Jacod, J. & Shiryaev, A. N. (1987). Limit theorems for stochastic processes. Springer, Berlin.
12. Karatzas, I. & Shreve, S. (1988). Brownian motion and stochastic calculus. Springer, New York.
13. Kalashnikov, V. & Norberg, R. (1999) Power tailed ruin probabilities in the presence of risky investments. Working Paper No. 159, Laboratory of Actuarial Mathematics, University of Copenhagen.
14. Lebedev, N. N. (1972). Special functions and their applications. Dover, New York.
15. Lehtonen, T. & Nyrhinen, H. (1992). Simulating level-crossing probabilities by importance sampling. Advances in Applied Probability 24, 858-874.
16. Lepingle, D. & Memin, J. (1978). Sur 1'integrabilite uniforme des martingales exponentielles. Zeitschrift fur Wahr scheinlichkeitstheorie and verwandte Gebiete 42, 175-204.
17. Nielsen, H.M. (1994) Generalization of Lundberg conjugation to processes with premiums depending on the reserve. Cand.act. dissertation (in Danish). Laboratory of Actuarial Mathematics, University of Copenhagen.
18. Nyrhinen, H. (2001). Finite and infinite time ruin probabilities in a stochastic economic environment. Stochastic Processes and their Applications 92, 265-285.
19. Ruohonen, M. (1980). On the probability of ruin of risk processes approximated by a diffusion process. Scandinavian Actuarial Journal 113-120.
20. Paulsen, J. (1993). Risk theory in a stochastic economic environment. Stochastic Processes and their Applications 46, 327-361.
21. Paulsen, J. (1998a). Ruin theory with compounding assets-a survey. Insurance: Mathematics and Economics 22, 3-16.
22. Paulsen, J. (1998b). Sharp conditions for certain ruin in a risk process with stochastic return on investments. Stochastic Processes and their Applications 75, 135-148.
23. Paulsen, J. & Gjessing, H. K. (1997). Ruin theory with stochastic return on investments. Advances in Applied Probability 29, 965-985.
24. Polyanin, A. D. & Zaitsev, V. F. (1995). Handbook of exact solutions for ordinary differential equations. CRC Press, Boca Raton, Florida.
25. Rydberg, T. H. (1997). The normal inverse Gaussian Levy process: simulation and approximation. Communications in Statistics, Stochastic Models 13, 887-910.
26. Siegmund, D. (1976). Importance sampling in the Monte Carlo study of sequential tests. Annals of Statistics 4, 914-924.
27. Slater, L. J. (1960). Confluent hyper geometric functions. Cambridge University Press, London.
28. Usabel, M. A. (1999). Efficient estimation of ultimate ruin probability. Actuarial Research Clearing House 1, 195-210.
29. Widder, D. V. (1971). An introduction to transform theory. Academic Press, New York.