Solving Optimal Stopping Problems via Randomization and Empirical Dual Optimization

Published Online:https://doi.org/10.1287/moor.2022.1306

References

  • [1] Andersen L (1999) A simple approach to the pricing of Bermudan swaptions in the multi-factor Libor market model. J. Comput. Finance 3(2):5–32.CrossrefGoogle Scholar
  • [2] Andersen L, Broadie M (2004) A primal-dual simulation algorithm for pricing multi-dimensional American options. Management Sci. 50(9):1222–1234.LinkGoogle Scholar
  • [3] Bartlett PL, Mendelson S (2006) Empirical minimization. Probab. Theory Related Fields 135(3):311–334.CrossrefGoogle Scholar
  • [4] Belomestny D (2013) Solving optimal stopping problems via empirical dual optimization. Ann. Appl. Probab. 23(5):1988–2019.CrossrefGoogle Scholar
  • [5] Belomestny D, Schoenmakers J (2018) Advanced Simulation-Based Methods for Optimal Stopping and Control (Palgrave Macmillan, London).CrossrefGoogle Scholar
  • [6] Belomestny D, Schoenmakers J (2021) From optimal martingales to randomized dual optimal stopping. Preprint, submitted February 2, https://arxiv.org/abs/2102.01533.Google Scholar
  • [7] Belomestny D, Bender C, Schoenmakers J (2009) True upper bounds for Bermudan products via non-nested Monte Carlo. Math. Finance 19(1):53–71.CrossrefGoogle Scholar
  • [8] Belomestny D, Hildebrand R, Schoenmakers J (2019) Optimal stopping via pathwise dual empirical maximisation. Appl. Math. Optim. 79(3):715–741.CrossrefGoogle Scholar
  • [9] Birman MS, Solomyak MZ (1967) Piecewise-polynomial approximations of functions of the classes wp,α. Sbornik: Math. 115(3):331–355.Google Scholar
  • [10] Bousquet O (2002) A Bennett concentration inequality and its application to suprema of empirical processes. Comptes Rendus Mathematique 334(6):495–500.CrossrefGoogle Scholar
  • [11] Broadie M, Cao M (2008) Improved lower and upper bound algorithms for pricing American options by simulation. Quant. Finance 8(8):845–861.CrossrefGoogle Scholar
  • [12] Broadie M, Glasserman P (2004) A stochastic mesh method for pricing high-dimensional American options. J. Comput. Finance 7(4):35–72.CrossrefGoogle Scholar
  • [13] Brown DB, Smith JE, Sun P (2010) Information relaxations and duality in stochastic dynamic programs. Oper. Res. 58(4, part 1):785–801.LinkGoogle Scholar
  • [14] Chandramouli SS (2019) A convex optimization approach to multiple stopping: Pricing chooser caps and swing options. Preprint, submitted October 30, http://dx.doi.org/10.2139/ssrn.3474273.Google Scholar
  • [15] Desai VV, Farias VF, Moallemi CC (2012) Pathwise optimization for optimal stopping problems. Management Sci. 58(12):2292–2308.LinkGoogle Scholar
  • [16] Friedman A (2008) Partial Differential Equations of Parabolic Type (Dover Publications, Mineola, NY).Google Scholar
  • [17] Giné E, Nickl R (2016) Mathematical Foundations of Infinite-Dimensional Statistical Models. Cambridge Series in Statistical and Probabilistic Mathematics (Cambridge University Press, New York).Google Scholar
  • [18] Glasserman P (2003) Monte Carlo Methods in Financial Engineering. Stochastic Modelling and Applied Probability, Vol. 53 (Springer, New York).CrossrefGoogle Scholar
  • [19] Haugh M, Kogan L (2004) Pricing American options: A duality approach. Oper. Res. 52(2):258–270.LinkGoogle Scholar
  • [20] Joshi M, Theis J (2002) Bounding Bermudan swaptions in a swap-rate market model. Quant. Finance 2(5):370–377.CrossrefGoogle Scholar
  • [21] Koltchinskii V (2011) Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems. Lecture Notes in Mathematics, Vol. 2033 (Springer, Berlin).CrossrefGoogle Scholar
  • [22] Lelong J (2018) Dual pricing of American options by Wiener chaos expansion. SIAM J. Financial Math. 9(2):493–519.CrossrefGoogle Scholar
  • [23] Liptser R, Shiryayev AN (1989) Theory of Martingales. Mathematics and Its Applications, Vol. 49 (Kluwer, Dordrecht, Netherlands).CrossrefGoogle Scholar
  • [24] Longstaff FA, Schwartz ES (2001) Valuing American options by simulation: A simple least-squares approach. Rev. Financial Stud. 14(1):113–147.CrossrefGoogle Scholar
  • [25] Nickl R, Pötscher B (2007) Bracketing metric entropy rates and empirical central limit theorems for function classes of Besov- and Sobolev-type. J. Theoret. Probab. 20(3):177–199.CrossrefGoogle Scholar
  • [26] Rogers LCG (2002) Monte Carlo valuation of American options. Math. Finance 12(3):271–286.CrossrefGoogle Scholar
  • [27] Rogers LCG (2007) Pathwise stochastic optimal control. SIAM J. Control Optim. 46(3):1116–1132.CrossrefGoogle Scholar
  • [28] Schoenmakers J, Zhang J, Huang J (2013) Optimal dual martingales, their analysis, and application to new algorithms for Bermudan products. SIAM J. Financial Math. 4(1):86–116.CrossrefGoogle Scholar
  • [29] Shapiro A (2003) Monte Carlo sampling methods. Ruszczyński A, Shapiro A, eds. Stochastic Programming. Handbooks in Operations Research and Management Science, Vol. 10 (Elsevier, Amsterdam), 353–425.CrossrefGoogle Scholar
  • [30] Tsitsiklis JN, Van Roy B (2001) Regression methods for pricing complex American style options. IEEE Trans. Neural Networks Learn. Systems 12(14):694–703.CrossrefGoogle Scholar
  • [31] Vidales MS, Siska D, Szpruch L (2018) Unbiased deep solvers for parametric PDEs. Preprint, submitted October 11, https://arxiv.org/abs/1810.05094.Google Scholar
  • [32] Viens FG, Vizcarra AB (2007) Supremum concentration inequality and modulus of continuity for sub-nth chaos processes. J. Functional Anal. 248(1):1–26.CrossrefGoogle Scholar
  • [33] Wang Y, Caflisch R (2010) Fast computation of upper bounds for American-style options without nested simulation. Preprint, submitted May 21, http://dx.doi.org/10.2139/ssrn.1612336.Google Scholar
  • [34] Yang B, Nadarajah S, Secomandi N (2019) Pathwise optimization for merchant energy production. Preprint, submitted December 28, https://arxiv.org/abs/1912.12525.Google Scholar
  • [35] Ye F, Zhou E (2015) Information relaxation and dual formulation of controlled Markov diffusions. IEEE Trans. Automatic Control 60(10):2676–2691.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.