Rare-event probability estimation with conditional Monte Carlo

Annals of Operations Research

Volumn 189, Issue 1, 2011, Pages 43-61

  Chan, Joshua C C ^a   Kroese, Dirk P ^a  

^a UNIVERSITY OF QUEENSLAND   (Australia)

Author keywords

Bottlenecks; Bounded relative error; Conditional Monte Carlo; Credit risks; Cross entropy; Degeneracy; Heavy tailed distribution; Normal copula; Rare event; Screening; Subexponential distribution; t copula

Indexed keywords

EID: 80052384350     PISSN: 02545330     EISSN: 15729338     Source Type: Journal    
DOI: 10.1007/s10479-009-0539-y     Document Type: Article

References (22)

1. Asmussen, S., & Binswanger, K. (1997). Simulation of ruin probabilities for subexponential claims. ASTIN Bulletin, 27, 297-318.
2. Asmussen, S., & Glynn, P. W. (2007). Stochastic simulation: algorithms and analysis. New York: Springer.
3. Asmussen, S., & Kroese, D. P. (2006). Improved algorithms for rare event simulation with heavy tails. Advances in Applied Probability, 38, 545-558.
4. Asmussen, S., Binswanger, K., & Højgaard, B. (2000). Rare events simulation for heavy-tailed distributions. Bernoulli, 6, 303-322.
5. Asmussen, S., Rubinstein, R. Y., & Kroese, D. P. (2005). Heavy tails, importance sampling and cross-entropy. Stochastic Models, 21, 57-76.
6. Bassmaboo, A., Juneja, S., & Zeevi, A. (2008). Portfolio credit risk with extremal dependence: Asymptotic analysis and efficient simulation. Operations Research, 56(3), 593-606.
7. Botev, Z. I., & Kroese, D. P. (2008). An efficient algorithm for rare-event probability estimation, combinatorial optimization, and counting. Methodology and Computing in Applied Probability, 10(4), 471-505.
8. Cruz, M. (2002). Modeling, measuring, and hedging operational risk. New York: Wiley.
9. Geweke, J. (1993). Bayesian treatment of the independent student-t linear model. Journal of Applied Econometrics, 8, S19-S40.
10. Glasserman, P. (2004). Monte Carlo methods in financial engineering. New York: Springer.
11. Glasserman, P., & Li, J. (2005). Importance sampling for portfolio credit risk. Management Science, 51(11), 1643-1656.
12. Glasserman, P., Heidelberger, P., & Shahabuddin, P. (2002). Portfolio value-at-risk with heavy-tailed risk factors. Mathematical Finance, 12(3), 239-269.
13. Goodman, L. A. (1962). The variance of the product of k random variables. Journal of the American Statistical Association, 57(297), 54-60.
14. Gupton, G., Finger, C., & Bhatia, M. (1997). Creditmetrics technical document (Technical report). J. P. Morgan & Co., New York.
15. Juneja, S. (2007). Estimating tail probabilities of heavy tailed distributions with asymptotically zero relative error. Queueing Systems, 57(2-3), 115-127.
16. Juneja, S., & Shahabuddin, P. (2002). Simulating heavy tailed processes using delayed hazard rate twisting. ACM Transactions on Modeling and Computer Simulation, 12(2), 94-118. ISSN 1049-3301.
17. Kroese, D. P., & Rubinstein, R. Y. (2004). The transform likelihood ratio method for rare event simulation with heavy tails. Queueing Systems, 46, 317-351.
18. Li, D. (2000). On default correlations: a copula function approach. Journal of Fixed Income, 9, 43-54.
19. Mashal, R., & Zeevi, A. (2002). Beyond correlation: Extreme co-movements between financial assets (Technical report). Columbia University, New York.
20. Rubinstein, R. Y. (2007). How to deal with the curse of dimensionality of likelihood ratios in Monte Carlo simulation (Technical report). Technion, Haifa, Israel.
21. Rubinstein, R. Y., & Kroese, D. P. (2004). The cross-entropy method: a unified approach to combinatorial optimization Monte-Carlo simulation, and machine learning. New York: Springer.
22. Rubinstein, R. Y., & Kroese, D. P. (2007). Simulation and the Monte Carlo method (2nd ed.). New York: Wiley.