A weak approximation for Bismut’s formula: : An algorithmic differentiation method
References
[1]
Baydin A.G., Pearlmutter B.A., Radul A.A., Siskind J.M., Automatic differentiation in machine learning: a survey, J. Mach. Learn. Res. 18 (2018) 1–43.
[2]
Bismut J.M., Large Deviations and the Malliavin Calculus, Birkhäuser, Basel, 1984.
[3]
Glasserman P., Monte Carlo Methods in Financial Engineering, Springer, New York, 2013.
[4]
Gobet E., Munos R., Sensitivity analysis using Itô-Malliavin calculus and martingales, and application to stochastic optimal control, SIAM J. Control Optim. 43 (5) (2005) 1676–1713.
[5]
Gyurkó L.G., Lyons T., Efficient and practical implementations of cubature on Wiener space, in: Stochastic Analysis 2010, Springer, New York, 2010, pp. 73–111.
[6]
Kloeden P.E., Platen E., Numerical Solution of Stochastic Differential Equations, Springer, New York, 1992.
[7]
Kusuoka S., Approximation of expectation of diffusion process and mathematical finance, in: Taniguchi Conference on Mathematics Nara’98, in: Advanced Studies in Pure Mathematics, Vol. 31, 2001, pp. 147–165.
[8]
Kusuoka S., Approximation of expectation of diffusion processes based on Lie algebra and Malliavin calculus, in: Advances in Mathematical Economics, Springer, Tokyo, 2004, pp. 69–83.
[9]
S. Kusuoka, D. Stroock, Applications of Malliavin Calculus, in: K. Itô (Ed.), Proceedings of the Taniguchi International Symposium on Stochastic Analysis, Kyoto and Katata, 1982, Vol. Part I, Kinokuniya, 1984, pp. 271–360.
[10]
Léandre R., Applications of the Malliavin calculus of bismut type without probability, WSEAS Trans. Math. 5 (11) (2006) 1205–1210.
[11]
Lejay A., The girsanov theorem without (so much) stochastic analysis, in: Séminaire de Probabilités XLIX, Vol. 2215, Springer, Cham, 2018.
[12]
Lyons T., Victoir N., Cubature on Wiener space, Proc. R. Soc. Lond. A 460 (2004) 169–198.
[13]
Mohamed S., Rosca M., Figurnov M., Mnih A., Monte Carlo gradient estimation in machine learning, J. Mach. Learn. Res. 21 (2020) 1–62.
[14]
Ninomiya S., Ninomiya M., A new higher-order weak approximation scheme for stochastic differential equations and the Runge–Kutta method, Finance Stoch. 13 (3) (2009) 415–443.
[15]
Ninomiya S., Victoir N., Weak approximation of stochastic differential equations and application to derivative pricing, Appl. Math. Finance 15 (2) (2008) 107–121.
[16]
Nualart D., The Malliavin Calculus and Related Topics, Springer, New York, 2006.
[17]
Reiman M.I., Weiss A., Sensitivity analysis for simulations via likelihood ratios, Oper. Res. 37 (5) (1989) 830–844.
[18]
Watanabe S., Lectures on Stochastic Differential Equations and Malliavin Calculus, Springer, Berlin, 1984.
[19]
Yamada T., Short communication: A Gaussian kusuoka-approximation without solving random ODEs, SIAM J. Financial Math. 13 (1) (2022) SC1–SC11.
[20]
Yang J., Kushner H.J., A Monte Carlo method for sensitivity analysis and parametric optimization of nonlinear stochastic systems, SIAM J. Control Optim. 29 (1991) 1216–1249.
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International Association for Mathematics and Computers in Simulation (IMACS).
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Elsevier Science Publishers B. V.
Netherlands
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Published: 01 February 2024
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