A FAST Method for Nested Estimation

Published Online:https://doi.org/10.1287/ijoc.2023.0118

References

  • Britten-Jones M, Schaefer SM (1999) Non-linear value-at-risk. Rev. Finance 2(2):161–187.CrossrefGoogle Scholar
  • Broadie M, Du Y, Moallemi CC (2011a) Efficient risk estimation via nested sequential simulation. Management Sci. 57(6):1172–1194.LinkGoogle Scholar
  • Broadie M, Du Y, Moallemi CC (2011b) Risk estimation via weighted regression. Proc. 2011 Winter Simulation Conf. (Institute of Electrical and Electronics Engineers, Piscataway, NJ), 3854–3865.Google Scholar
  • Broadie M, Du Y, Moallemi CC (2015) Risk estimation via regression. Oper. Res. 63(5):1077–1097.LinkGoogle Scholar
  • Cheng HF, Zhang K (2021) Non-nested estimators for the central moments of a conditional expectation and their convergence properties. Oper. Res. Lett. 49(5):625–632.CrossrefGoogle Scholar
  • Cheng HF, Liu X, Zhang K (2022) Constructing confidence intervals for nested simulation. Naval Res. Logist. 69:1138–1149.CrossrefGoogle Scholar
  • Choe Y, Byon E, Chen N (2015) Importance sampling for reliability evaluation with stochastic simulation models. Technometrics 57(3):351–361.CrossrefGoogle Scholar
  • Corlu CG, Akcay A, Xie W (2020) Stochastic simulation under input uncertainty: A review. Oper. Res. Perspect. 7:100162.CrossrefGoogle Scholar
  • Duffie D, Pan J (2001) Analytical value-at-risk with jumps and credit risk. Finance Stochastics 5(2):155–180.CrossrefGoogle Scholar
  • Glasserman P (2004) Monte Carlo Methods in Financial Engineering, vol. 53 (Springer, New York).Google Scholar
  • Glasserman P, Heidelberger P, Shahabuddin P (2000) Variance reduction techniques for estimating value-at-risk. Management Sci. 16(10):1349–1364.LinkGoogle Scholar
  • Glasserman P, Heidelberger P, Shahabuddin P (2002) Portfolio value-at-risk with heavy-tailed risk factors. Math. Finance 12(3):239–269.CrossrefGoogle Scholar
  • Goda T (2017) Computing the variance of a conditional expectation via non-nested Monte Carlo. Oper. Res. Lett. 45(1):63–67.CrossrefGoogle Scholar
  • Goda T, Hironaka T, Iwamoto T (2020) Multilevel Monte Carlo estimation of expected information gains. Stochastic Anal. Appl. 38(4):581–600.CrossrefGoogle Scholar
  • Gordy M, Juneja S (2006) Efficient simulation for risk measurement in portfolio of CDOs. Proc. 2006 Winter Simulation Conf. (Institute of Electrical and Electronics Engineers, Piscataway, NJ), 749–756.Google Scholar
  • Gordy MB, Juneja S (2010) Nested simulation in portfolio risk measurement. Management Sci. 56(10):1833–1848.LinkGoogle Scholar
  • Hong LJ, Juneja S (2009) Estimating the mean of a non-linear function of conditional expectation. Proc. 2009 Winter Simulation Conf. (Institute of Electrical and Electronics Engineers, Piscataway, NJ), 1223–1236.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.LinkGoogle Scholar
  • Huan X, Marzouk YM (2013) Simulation-based optimal Bayesian experimental design for nonlinear systems. J. Comput. Phys. 232(1):288–317.CrossrefGoogle Scholar
  • Lan H, Nelson BL, Staum J (2010) A confidence interval procedure for expected shortfall risk measurement via two-level simulation. Oper. Res. 58(5):1481–1490.LinkGoogle Scholar
  • Lee SH (1998) Monte Carlo computation of conditional expectation quantiles. Unpublished PhD thesis, Stanford University, Stanford, CA.Google Scholar
  • Lee SH, Glynn PW (2003) Computing the distribution function of a conditional expectation via Monte Carlo: Discrete conditioning spaces. ACM Trans. Modeling Comput. Simulation 13(3):238–258.CrossrefGoogle Scholar
  • Liang G, Zhang K, Luo J, (2024) GitHub repository: A FAST method for nested estimation. https://dx.doi.org/10.1287/ijoc.2023.0118.cd, https://github.com/INFORMSJoC/2023.0118.Google Scholar
  • Liu M, Staum J (2010) Stochastic kriging for efficient nested simulation of expected shortfall. J. Risk 12(3):3–27.CrossrefGoogle Scholar
  • Liu X, Yan X, Zhang K (2024) Kernel quantile estimators for nested simulation with application to portfolio value-at-risk measurement. Eur. J. Oper. Res. 312(3):1168–1177.CrossrefGoogle Scholar
  • Quenouille MH (1956) Notes on bias in estimation. Biometrika 43(3–4):353–360.CrossrefGoogle Scholar
  • Rainforth T (2017) Automating inference, learning, and design using probabilistic programming. Unpublished PhD thesis, University of Oxford, Oxford, UK.Google Scholar
  • Rainforth T, Cornish R, Yang H, Warrington A, Wood F (2018) On nesting Monte Carlo estimators. Internat. Conf. Machine Learning (PMLR, New York), 4267–4276.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.LinkGoogle Scholar
  • Wang W, Wang Y, Zhang X (2024) Smooth nested simulation: Bridging cubic and square root convergence rates in high dimensions. Management Sci. Forthcoming.LinkGoogle Scholar
  • Yi Y, Xie W (2017) An efficient budget allocation approach for quantifying the impact of input uncertainty in stochastic simulation. ACM Trans. Modeling Comput. Simulation 27(4):1–23.CrossrefGoogle Scholar
  • Zhang K, Liu G, Wang S (2022b) Bootstrap-based budget allocation for nested simulation. Oper. Res. 70(2):1128–1142.LinkGoogle Scholar
  • Zhang K, Feng BM, Liu G, Wang S (2022a) Sample recycling for nested simulation with application in portfolio risk measurement. Preprint, submitted March 29, 2022, https://arxiv.org/abs/2203.15929.Google Scholar
  • Zhu H, Liu T, Zhou E (2020) Risk quantification in stochastic simulation under input uncertainty. ACM Trans. Modeling Comput. Simulation 30(1):1–24.CrossrefGoogle Scholar
INFORMS site uses cookies to store information on your computer. Some are essential to make our site work; Others help us improve the user experience. By using this site, you consent to the placement of these cookies. Please read our Privacy Statement to learn more.