A New Unbiased Stochastic Derivative Estimator for Discontinuous Sample Performances with Structural Parameters

Published Online:https://doi.org/10.1287/opre.2017.1674

References

  • Andrieu L, Cohen G, Vázquez-Abad FJ (2010) Gradient-based simulation optimization under probability constraints. Eur. J. Oper. Res. 212(2):345–351.CrossrefGoogle Scholar
  • Asmussen S, Glynn PW (2007) Stochastic Simulation: Algorithms and Analysis, Vol. 57 (Springer, New York).CrossrefGoogle Scholar
  • Broadie M, Glasserman P (1996) Estimating security price derivatives using simulation. Management Sci. 42(2):269–285.LinkGoogle Scholar
  • Cao X-R, Wan X (2014) Sensitivity analysis of nonlinear behavior with distorted probability. Math. Finance 27(1):115–150.CrossrefGoogle Scholar
  • Chen N, Glasserman P (2007) Malliavin Greeks without Malliavin calculus. Stochastic Processes and Their Appl. 117(11):1689–1723.CrossrefGoogle Scholar
  • Evans LC (1998) Partial Differential Equations (American Mathematical Society, Providence, RI).Google Scholar
  • Fournié E, Lasry J-M, Lebuchoux J, Lions P-L, Touzi N (1999) Applications of Malliavin calculus to Monte Carlo methods in finance. Finance and Stochastics 3(4):391–412.CrossrefGoogle Scholar
  • Fu MC (1994) Sample path derivatives for (s, S) inventory systems. Oper. Res. 42(2):351–364.LinkGoogle Scholar
  • Fu MC (2006) Gradient estimation. Henderson SG, Nelson BL, eds. Handbooks in Operations Research and Management Science, Vol. 13 (Elsevier, Amsterdam), 575–616.Google Scholar
  • Fu MC (2008) What you should know about simulation and derivatives. Naval Res. Logist. 55(8):723–736.CrossrefGoogle Scholar
  • Fu MC (2015) Stochastic gradient estimation. Fu MC, ed. Handbook of Simulation Optimization, Vol. 216 (Springer, New York), 105–147.CrossrefGoogle Scholar
  • Fu MC, Hu J-Q (1993) Second derivative sample path estimators for the GI/G/m queue. Management Sci. 39(3):359–383.LinkGoogle Scholar
  • Fu MC, Hu J-Q (1995) Sensitivity analysis for Monte Carlo simulation of option pricing. Probab. Engrg. Informational Sci. 9(3):417–446.CrossrefGoogle Scholar
  • Fu MC, Hu J-Q (1997) Conditional Monte Carlo: Gradient Estimation and Optimization Applications (Kluwer Academic Publishers, Boston).CrossrefGoogle Scholar
  • Fu MC, Hu J-Q (1999) Efficient design and sensitivity analysis of control charts using Monte Carlo simulation. Management Sci. 45(3):395–413.LinkGoogle Scholar
  • Fu MC, Hong LJ, Hu J-Q (2009) Conditional Monte Carlo estimation of quantile sensitivities. Management Sci. 55(12):2019–2027.LinkGoogle Scholar
  • Glasserman P (1991) Gradient Estimation via Perturbation Analysis (Kluwer Academic Publishers, Boston).Google Scholar
  • Glasserman P, Gong W-B (1990) Smoothed perturbation analysis for a class of discrete-event systems. IEEE Trans. Automatic Control 35(11):1218–1230.CrossrefGoogle Scholar
  • Gong W-B, Ho Y-C (1987) Smoothed perturbation analysis of discrete event dynamical systems. IEEE Trans. Automatic Control 32(10):858–866.CrossrefGoogle Scholar
  • Heidergott B (1999) Optimisation of a single-component maintenance system: A smoothed perturbation analysis approach. Eur. J. Oper. Res. 119(1):181–190.CrossrefGoogle Scholar
  • Heidergott B (2001) Option pricing via Monte Carlo simulation: A weak derivative approach. Probab. Engrg. Informational Sci. 15(3):335–349.CrossrefGoogle Scholar
  • Heidergott B, Leahu H (2010) Weak differentiability of product measures. Math. Oper. Res. 35(1):27–51.LinkGoogle Scholar
  • Heidergott B, Volk-Makarewicz W (2016) A measure-valued differentiation approach to sensitivity analysis of quantiles. Math. Oper. Res. 41(1):293–317.LinkGoogle Scholar
  • Ho Y-C, Cao X-R (1991) Discrete Event Dynamic Systems and Perturbation Analysis (Kluwer Academic Publishers, Boston).CrossrefGoogle Scholar
  • Hong LJ, Liu G (2009) Simulating sensitivities of conditional value at risk. Management Sci. 55(2):281–293.LinkGoogle Scholar
  • Hong LJ, Liu G (2010) Pathwise estimation of probability sensitivities through terminating or steady-state simulations. Oper. Res. 58(2):357–370.LinkGoogle Scholar
  • Jiang G, Fu MC (2015) Technical note—On estimating quantile sensitivities via infinitesimal perturbation analysis. Oper. Res. 63(2):435–441.LinkGoogle Scholar
  • Kushner HJ, Yin GG (2003) Stochastic Approximation and Recursive Algorithms and Applications (Springer, New York).Google Scholar
  • Lang S (2013) Undergraduate Analysis (Springer, New York).Google Scholar
  • L’Ecuyer P (1990) A unified view of the IPA, SF, and LR gradient estimation techniques. Management Sci. 36(11):1364–1383.LinkGoogle Scholar
  • L’Ecuyer P, Perron G (1994) On the convergence rates of IPA and FDC derivative estimators. Oper. Res. 42(4):643–656.LinkGoogle Scholar
  • Liu G, Hong LJ (2011) Kernel estimation of the Greeks for options with discontinuous payoffs. Oper. Res. 59(1):96–108.LinkGoogle Scholar
  • Peng Y, Fu MC, Hu J-Q (2016a) Estimating distribution sensitivity using generalized likelihood ratio method. Cassandras CG, Giua A, Li Z, eds. Proc. 13th Internat. Workshop on Discrete Event Systems, WODES ’16 (IEEE, Piscataway, NJ), 123–128.Google Scholar
  • Peng Y, Fu MC, Hu J-Q (2016b) On the regularity conditions and applications for generalized likelihood ratio method. Proc. Winter Simulation Conf., WSC ’16 (IEEE, Piscataway, NJ), 919–930.Google Scholar
  • Peng Y, Fu MC, Glynn PW, Hu J-Q (2017) On the asymptotic analysis of quantile sensitivity estimation by Monte Carlo simulation. Proc. Winter Simulation Conf., WSC ’17 (IEEE, Piscataway, NJ).Google Scholar
  • Pflug GC (1996) Optimization of Stochastic Models (Kluwer Academic, Boston).CrossrefGoogle Scholar
  • Rubinstein RY, Shapiro A (1993) Discrete Event Systems: Sensitivity Analysis and Stochastic Optimization by the Score Function Method (John Wiley & Sons, New York).Google Scholar
  • Rudin W (1987) Real and Complex Analysis (McGraw-Hill Education, New York).Google Scholar
  • Wang Y, Fu MC, Marcus SI (2012) A new stochastic derivative estimator for discontinuous payoff functions with application to financial derivatives. Oper. Res. 60(2):447–460.LinkGoogle 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.