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Statistical tools for simulation design and analysis: simulating ruin probabilities in insurance risk processes with subexponential claims

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Winter Simulation Conference archive
Proceedings of the 33nd conference on Winter simulation table of contents

Arlington, Virginia

SESSION: Analysis methodology table of contents

Pages: 468 - 476

Year of Publication: 2001

ISBN:0-7803-7309-X

Authors

Nam Kyoo Boots	Vrije Universiteit, De Boelelaan 1105, Amsterdam, 1081 HV, THE NETHERLANDS
Perwez Shahabuddin	Columbia University, New York, NY

Sponsors

INFORMS/CS : Institute for Operations Research and the Management Sciences/College on Simulation
IEEE/SMCS : Institute of Electrical and Electronics Engineers/Systems, Man, and Cybernetics Society
NIST : National Institute of Standards and Technology
ACM: Association for Computing Machinery
SCS : The Society for Computer Simulation International
SIGSIM: ACM Special Interest Group on Simulation and Modeling
IIE : Institute of Industrial Engineers
IEEE/CS : Institute of Electrical and Electronics Engineers/Computer Society
ASA : American Statistical Association

Publisher

IEEE Computer Society Washington, DC, USA

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ABSTRACT

We describe a fast simulation framework for simulating small ruin probabilities in insurance risk processes with subexponential claims. Naive simulation is inefficient since the event of interest is rare, and special simulation techniques like importance sampling need to be used. An importance sampling change of measure known as sub-exponential twisting has been found useful for some rare event simulations in the subexponential context. We describe conditions that are sufficient to ensure that the infinite horizon probability can be estimated in a (work-normalized) large set asymptotically optimal manner, using this change of measure. These conditions are satisfied for some large classes of insurance risk processes --- e.g., processes with Markov-modulated claim arrivals and claim sizes --- where the heavy tails are of the 'Weibull type'. We also give much weaker conditions for the estimation of the finite horizon ruin probability. Finally, we present experiments supporting our results.

REFERENCES

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	1	Asmussen, S. 1985. Conjugate processes and the simulation of ruin problems. Stochastic Processes and their Applications 20: 213-229.
	2	Asmussen, S. 2000. Ruin Probabilities. World Scientific, Singapore, New Jersey, London, Hong Kong.
	3	Asmussen, S., and K. Binswanger. 1997. Simulation of ruin probabilities for subexponential claims. ASTIN Bulletin 27 (2): 297-318.
	4	Asmussen, S., K. Binswanger and B. Hojgaard. 2000. Rare event simulation for heavy-tailed distributions. Bernoulli 6 (2): 303-322.
	5	Asmussen, S., L. F. Henriksen, and C. Klüppelberg. 1994. Large claims approximations for risk processes in a Markovian environment. Stochastic Processes and their Applications 54: 29-43.
	6	Asmussen, S., and B. Hojgaard. 1996. Finite horizon ruin probabilities for Markov-modulated risk processes with heavy tails. Th. Random Processes, 2: 96-107.
	7	Asmussen, S., and C. Klüppelberg. 1996. Large deviations results for subexponential tails, with applications to insurance risk. Stochastic Processes and their Applications 64: 103-125.
	8	Asmussen, S., H. Schmidli, and V. Schmidt. 1999. Tail probabilities for non-standard risk and queueing processes with subexponential jumps. Advances in Applied Probability 31: 422-447.
	9	Nam Kyoo Boots , Perwez Shahabuddin, Simulating GI/GI/1 queues and insurance risk processes with subexponential distributions, Proceedings of the 32nd conference on Winter simulation, December 10-13, 2000, Orlando, Florida
	10	Boots, N. K., and P. Shahabuddin. 2000b. Simulating tail probabilities in GI/GI/1 queues and insurance risk processes with subexponential distributions. Research Report, Dept. of Industrial Engineering and Operations Research, Columbia University, NY 10027.
	11	Boots, N. K., and P. Shahabuddin. 2001. A framework for simulating small ruin probabilities in insurance risk processes with subexponential distributions. Research Report, Dept. of Industrial Engineering and Operations Research, Columbia University, NY 10027.
	12	Bucklew, J. A. 1990. Large Deviations Techniques in Decision, Simulation, and Estimation. John Wiley & Sons, Inc.
	13	Cottrell, M., J. C. Fort and G. Malgouyres. 1983. Large deviations and rare events in the study of stochastic algorithms. IEEE Transactions on Automatic Control AC28: 907-920.
	14	Chistyakov, V. P. 1964. A theorem on sums of independent positive random variables and its applications to branching processes. Theory of Probability and its Applications 9: 640-648.
	15	Paul Embrechts , Thomas Mikosch , Claudia Klüppelberg, Modelling extremal events: for insurance and finance, Springer-Verlag, London, 1997
	16	Embrechts, P., and C. Klüppelberg. 1993. Some aspects of insurance mathematics. Theory of Probability and its Applications 38 (2): 262-295.
	17	Embrechts, P., and N. Veraverbeke. 1982. Estimates for the probability of ruin with the special emphasis on the possibility of large claims. Insurance: Mathematics and Economics 1: 55-72.
	18	Peter W. Glynn , Ward Whitt, The asymptotic efficiency of simulation estimators, Operations Research, v.40 n.3, p.505-520, May–June 1992 [doi>10.1287/opre.40.3.505]
	19	Goldie, C. M., and S. Resnick. 1988. Distributions that are both subexponential and in the domain of attraction of an extreme-value distribution. Advances in Applied Probability 20: 706-718.
	20	Jelenković, P., and A. A. Lazar. 1998. Subexponential asymptotics for a Markov-modulated random walk with a queueing application. Journal of Applied Probability 35: 325-347.
	21	Juneja, S., and P. Shahabuddin. 1999. Simulating heavy-tailed processes using delayed hazard rate twisting. Research Report, Dept. of Industrial Engineering and Operations Research, Columbia University, NY 10027.
	22	Philip Heidelberger, Fast simulation of rare events in queueing and reliability models, ACM Transactions on Modeling and Computer Simulation (TOMACS), v.5 n.1, p.43-85, Jan. 1995 [doi>10.1145/203091.203094]
	23	Lehtohnen, T., and H. Nyrhinen. 1992. Simulating level-crossing probabilities by importance sampling. Advances in Applied Probability 24: 858-874.
	24	Pakes, A. G. 1975. On the tails of waiting time distributions. Journal of Applied Probability 12: 555-564.
	25	Sadowsky, J. S. 1991. Large deviations and efficient estimation of excessive backlogs in GI/G/m queue. IEEE Transactions on Automatic Control 36 (1991): 1383-1394.
	26	Perwez Shahabuddin, Importance sampling for the simulation of highly reliable Markovian systems, Management Science, v.40 n.3, p.333-352, March 1994 [doi>10.1287/mnsc.40.3.333]
	27	Siegmund, D. 1976. Importance sampling in the Monte Carlo study of sequential tests. The Annals of Statistics 4: 673-684.