Randomized Dimension Reduction for Monte Carlo Simulations

Published Online:https://doi.org/10.1287/mnsc.2018.3250

References

  • Acworth PA, Broadie M, Glasserman P (1998) A comparison of some Monte Carlo and quasi Monte Carlo techniques for option pricing. Niederreiter H, Hellekalek P, Larcher G, Zinterhof P, eds. Monte Carlo and Quasi-Monte Carlo Methods 1996, Lecture Notes in Statistics, vol. 127 (Springer, New York), 1–18.CrossrefGoogle Scholar
  • Åkesson F, Lehoczky JP (2000) Path generation for quasi-Monte Carlo simulation of mortgage-backed securities. Management Sci. 46(9):1171–1187.LinkGoogle Scholar
  • Andrew AM (1979) Another efficient algorithm for convex hulls in two dimensions. Inform. Processing Lett. 9(5):216–219.CrossrefGoogle Scholar
  • Asmussen S, Glynn PW (2007) Stochastic Simulation: Algorithms and Analysis, vol. 57 (Springer Science & Business Media, New York).CrossrefGoogle Scholar
  • Billingsley P (1999) Convergence of Probability Measures, 2nd ed. (Wiley, New York).CrossrefGoogle Scholar
  • Blanchet J, Leder K, Shi Y (2011) Analysis of a splitting estimator for rare event probabilities in jackson networks. Stochastic Systems 1(2):306–339.LinkGoogle Scholar
  • Botev ZI, L’Ecuyer P, Rubino G, Simard R, Tuffin B (2013) Static network reliability estimation via generalized splitting. INFORMS J. Comput. 25(1):56–71.LinkGoogle Scholar
  • Caflisch RE (1998) Monte Carlo and quasi-Monte Carlo methods. Acta Numer. 7:1–49.CrossrefGoogle Scholar
  • Caflisch RE, Morokoff WJ, Owen AB (1997) Valuation of mortgage backed securities using Brownian bridges to reduce effective dimension. J. Comput. Finance 1(1):27–46.CrossrefGoogle Scholar
  • Ermakov S, Melas V (1995) Design and Analysis of Simulation Experiments, vol. 339 (Springer Science & Business Media, Dordrecht, Netherlands).Google Scholar
  • Feldman Z, Mandelbaum A, Massey WA, Whitt W (2008) Staffing of time-varying queues to achieve time-stable performance. Management Sci. 54(2):324–338.LinkGoogle Scholar
  • Giles MB (2008) Multilevel Monte Carlo path simulation. Oper. Res. 56(3):607–617.LinkGoogle Scholar
  • Glasserman P (2004) Monte Carlo Methods in Financial Engineering, vol. 53 (Springer, New York).Google Scholar
  • Glasserman P, Heidelberger P, Shahabuddin P (1999a) Asymptotically optimal importance sampling and stratification for pricing path-dependent options. Math. Finance 9(2):117–152.CrossrefGoogle Scholar
  • Glasserman P, Heidelberger P, Shahabuddin P, Zajic T (1999b) Multilevel splitting for estimating rare event probabilities. Oper. Res. 47(4):585–600.LinkGoogle Scholar
  • Glynn PW, Rhee C-H (2014) Exact estimation for Markov chain equilibrium expectations. J. Appl. Probab. 51(A):377–389.CrossrefGoogle Scholar
  • Glynn PW, Whitt W (1992) The asymptotic efficiency of simulation estimators. Oper. Res. 40(3):505–520.LinkGoogle Scholar
  • Hull J (2014) Options, Futures and Other Derivatives, 9th ed. (Prentice-Hall, Upper Saddle River, NJ).Google Scholar
  • Imai J, Tan KS (2006) A general dimension reduction technique for derivative pricing. J. Comput. Finance 10(2):129–155.CrossrefGoogle Scholar
  • Jiang G, Fu MC (2017) Importance splitting for finite-time rare event simulation. IEEE Trans. Automatic Control 63(6):1760–1767.CrossrefGoogle Scholar
  • Kahalé N (2016) Optimized sampling for Monte Carlo simulations via dimension reduction. Proc. 9th NIPS Workshop Optim. Machine Learn., Barcelona, Spain.Google Scholar
  • L’Ecuyer P, Lécot C, Tuffin B (2008) A randomized quasi-Monte Carlo simulation method for Markov chains. Oper. Res. 56(4):958–975.LinkGoogle Scholar
  • L’Ecuyer P, Lemieux C (2000) Variance reduction via lattice rules. Management Sci. 46(9):1214–1235.LinkGoogle Scholar
  • Liu R, Owen AB (2006) Estimating mean dimensionality of analysis of variance decompositions. J. Amer. Statist. Assoc. 101(474):712–721.CrossrefGoogle Scholar
  • Ma N, Whitt W (2017) A rare-event simulation algorithm for periodic single-server queues. INFORMS J. Comput. 30(1):71–89.LinkGoogle Scholar
  • Nagel K, Wagner P, Woesler R (2003) Still flowing: Approaches to traffic flow and traffic jam modeling. Oper. Res. 51(5):681–710.LinkGoogle Scholar
  • Owen AB (2003) The dimension distribution and quadrature test functions. Statistica Sinica 13(1):1–18.Google Scholar
  • Paxson V (1994) Empirically derived analytic models of wide-area TCP connections. IEEE/ACM Trans. Networking (TON) 2(4):316–336.CrossrefGoogle Scholar
  • Revuz D, Yor M (1999) Continuous Martingales and Brownian Motion, 3rd ed. (Springer, Berlin).CrossrefGoogle Scholar
  • Rhee C-H, Glynn PW (2015) Unbiased estimation with square root convergence for SDE models. Oper. Res. 63(5):1026–1043.LinkGoogle Scholar
  • Rosenbaum I, Staum J (2017) Multilevel Monte Carlo metamodeling. Oper. Res. 65(4):1062–1077.LinkGoogle Scholar
  • Rubinstein RY, Kroese DP (2016) Simulation and the Monte Carlo Method, vol. 10 (John Wiley & Sons, Hoboken, NJ).CrossrefGoogle Scholar
  • Shiryaev AN (1996) Probability. Axler S, Ribet K, eds. Graduate Texts in Mathematics, vol. 95 (Springer, New York).Google Scholar
  • Sloan IH, Woźniakowski H (1998) When are quasi-Monte Carlo algorithms efficient for high dimensional integrals? J. Complexity 14(1):1–33.CrossrefGoogle Scholar
  • Sobol IM (2001) Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates. Math. Comput. Simulation 55(1–3):271–280.CrossrefGoogle Scholar
  • Thompson K, Miller GJ, Wilder R (1997) Wide-area internet traffic patterns and characteristics. IEEE Network 11(6):10–23.CrossrefGoogle Scholar
  • Wang X (2006) On the effects of dimension reduction techniques on some high-dimensional problems in finance. Oper. Res. 54(6):1063–1078.LinkGoogle Scholar
  • Wang X, Fang KT (2003) The effective dimension and quasi-Monte Carlo integration. J. Complexity 19(2):101–124.CrossrefGoogle Scholar
  • Wang X, Sloan IH (2005) Why are high-dimensional finance problems often of low effective dimension? SIAM J. Sci. Comput. 27(1):159–183.CrossrefGoogle Scholar
  • Wang X, Sloan IH (2011) Quasi-Monte Carlo methods in financial engineering: An equivalence principle and dimension reduction. Oper. Res. 59(1):80–95.LinkGoogle Scholar
  • Wang X, Tan KS (2013) Pricing and hedging with discontinuous functions: quasi-Monte Carlo methods and dimension reduction. Management Sci. 59(2):376–389.LinkGoogle Scholar
  • Whitt W (2017) Time-varying queues. Working paper, Columbia University, New York.Google Scholar
  • Whitt W, You W (2016) Time-varying robust queueing. Working paper, Columbia University, New York.Google Scholar
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