Efficient Nested Simulation Experiment Design via the Likelihood Ratio Method

References

• Barton RR, Lam H, Song E (2022) Input uncertainty in stochastic simulation. Salhi S, Boylan J, eds. The Palgrave Handbook of Operations Research (Springer International Publishing, Cham, Switzerland), 573–620.Crossref, Google Scholar
• Broadie M, Du Y, Moallemi CC (2011) Efficient risk estimation via nested sequential simulation. Management Sci. 57(6):1172–1194.Link, Google Scholar
• Broadie M, Du Y, Moallemi CC (2015) Risk estimation via regression. Oper. Res. 63(5):1077–1097.Link, Google Scholar
• Dang O, Feng M, Hardy MR (2022) Dynamic importance allocated nested simulation for variable annuity risk measurement. Ann. Actuarial Sci. 16(2):319–348.Crossref, Google Scholar
• Dong J, Feng M, Nelson BL (2018) Unbiased metamodeling via likelihood ratios. Rabe M, Juan AA, Mustafee N, Skoogh A, Jain S, Johansson B, eds. Proc. 2018 Winter Simulation Conf. (IEEE, Piscataway, NJ), 1778–1789.Google Scholar
• Elvira V, Martino L, Robert CP (2018) Rethinking the effective sample size. Preprint, submitted September 11, https://arxiv.org/abs/1809.04129.Google Scholar
• Feng M, Song E (2019) Efficient input uncertainty quantification via green simulation using sample path likelihood ratios. Mustafee N, Bae K-HG, Lazarova-Molnar S, Rabe M, Szabo C, Haas P, Son Y-J, eds. Proc. 2019 Winter Simulation Conf. (IEEE, Piscataway, NJ), 3693–3704.Google Scholar
• Feng BM, Song E (2024) Efficient nested simulation experiment design via the likelihood ratio method. http://dx.doi.org/10.1287/ijoc.2022.0392.cd, https://github.com/INFORMSJoC/2022.0392/.Google Scholar
• Feng M, Staum J (2015) Green simulation designs for repeated experiments. Yilmaz L, Chan WKV, Moon I, Roeder TMK, Macal C, Rossetti MD, eds. Proc. 2015 Winter Simulation Conf. (IEEE, Piscataway, NJ), 403–413.Google Scholar
• Feng M, Staum J (2017) Green simulation: Reusing the output of repeated experiments. ACM Trans. Model. Comput. Simulation 27(4):1–28.Crossref, Google Scholar
• Fu MC (2015) Handbook of Simulation Optimization (Springer, New York).Crossref, Google Scholar
• Giles MB, Haji-Ali AL (2019) Multilevel nested simulation for efficient risk estimation. SIAM/ASA J. Uncertainty Quantification 7(2):497–525.Crossref, Google Scholar
• Glasserman P (2003) Monte Carlo Methods in Financial Engineering (Springer, Cham, Switzerland).Crossref, Google Scholar
• Glasserman P, Xu X (2014) Robust risk measurement and model risk. Quant. Finance 14(1):29–58.Crossref, Google Scholar
• Gordy MB, Juneja S (2010) Nested simulation in portfolio risk measurement. Management Sci. 56(10):1833–1848.Link, Google Scholar
• Ha H, Bauer D (2022) A least-squares Monte Carlo approach to the estimation of enterprise risk. Finance Stochastics 26(3):417–459.Crossref, Google Scholar
• Heidelberger P, Lewis PAW (1984) Quantile estimation in dependent sequences. Oper. Res. 32(1):185–209.Link, Google Scholar
• Hesterberg TC (1988) Advances in importance sampling. PhD thesis, Stanford University, Stanford, CA.Google Scholar
• Hong LJ, Juneja S, Liu G (2017) Kernel smoothing for nested estimation with application to portfolio risk measurement. Oper. Res. 65(3):657–673.Link, Google Scholar
• Kleijnen JP, Rubinstein RY (1996) Optimization and sensitivity analysis of computer simulation models by the score function method. Eur. J. Oper. Res. 88(3):413–427.Crossref, Google Scholar
• Kong A (1992) A note on importance sampling using standardized weights. Technical Report No. 348, Department of Statistics, University of Chicago, Chicago.Google Scholar
• L’Ecuyer P (1990) A unified view of the IPA, SF, and LR gradient estimation techniques. Management Sci. 36(11):1364–1383.Link, Google Scholar
• L’Ecuyer P (1993) Two approaches for estimating the gradient in functional form. Evans GW, Mollaghasemi M, Russell EC, Biles WE, eds. Proc. 1993 Winter Simulation Conf. (IEEE, Piscataway, NJ), 338–346.Google Scholar
• Lee S (1998) Monte Carlo computation of conditional expectation quantiles. PhD thesis, Stanford University, Department of Engineering–Economic Systems and Operations Research, Stanford, CA.Google Scholar
• Li P, Feng R (2021) Nested Monte Carlo simulation in financial reporting: A review and a new hybrid approach. Scandinavian Actuarial J. 2021(9):744–778.Crossref, Google Scholar
• Liu JS (1996) Metropolized independent sampling with comparisons to rejection sampling and importance sampling. Statist. Comput. 6(2):113–119.Crossref, Google Scholar
• Liu M, Staum J (2010) Stochastic kriging for efficient nested simulation of expected shortfall. J. Risk 12(3):3–27.Crossref, Google Scholar
• Longstaff FA, Schwartz ES (2001) Valuing American options by simulation: A simple least-squares approach. Rev. Financial Stud. 14(1):113–147.Crossref, Google Scholar
• Maggiar A, Waechter A, Dolinskaya IS, Staum J (2018) A derivative-free trust-region algorithm for the optimization of functions smoothed via Gaussian convolution using adaptive multiple importance sampling. SIAM J. Optim. 28(2):1478–1507.Crossref, Google Scholar
• Martino L, Elvira V, Louzada F (2017) Effective sample size for importance sampling based on discrepancy measures. Signal Processing 131:386–401.Crossref, Google Scholar
• Owen AB (2013) Monte Carlo theory, methods and examples. Accessed June 6, 2024, https://artowen.su.domains/mc/.Google Scholar
• Risk J, Ludkovski M (2018) Sequential design and spatial modeling for portfolio tail risk measurement. SIAM J. Financial Math. 9(4):1137–1174.Crossref, Google Scholar
• Rockafellar RT, Uryasev S (2002) Conditional value-at-risk for general loss distributions. J. Banking Finance 26(7):1443–1471.Crossref, Google Scholar
• Rubinstein RY, Shapiro A (1993) Discrete Event Systems: Sensitivity Analysis and Stochastic Optimization by the Score Function Method (John Wiley & Sons, Hoboken, NJ).Google Scholar
• Sen PK (1972) On the bahadur representation of sample quantiles for sequences of ϕ-mixing random variables. J. Multivariate Anal. 2(1):77–95.Crossref, Google Scholar
• Song E, Wu-Smith P, Nelson BL (2020) Uncertainty quantification in vehicle content optimization for general motors. INFORMS J. Appl. Analytics 50(4):225–238.Link, Google Scholar
• Sun Y, Apley DW, Staum J (2011) Efficient nested simulation for estimating the variance of a conditional expectation. Oper. Res. 59(4):998–1007.Link, Google Scholar
• Wang W, Wang Y, Zhang X (2024) Smooth nested simulation: Bridging cubic and square root convergence rates in high dimensions. Management Sci., ePub ahead of print March 20, https://doi.org/10.1287/mnsc.2022.00204.Google Scholar
• Zhang K, Feng BM, Liu G, Wang S (2022) Sample recycling for nested simulation with application in portfolio risk measurement. Preprint, submitted March 29, https://arxiv.org/abs/2203.15929.Google Scholar
• Zhou E, Liu T (2019) Online quantification of input model uncertainty by two-layer importance sampling. Preprint, submitted December 24, https://arxiv.org/abs/1912.11172.Google Scholar