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We propose a new forward-backward stochastic differential equation solver for high-dimensional derivatives pricing problems by combining deep learning solver with least square regression technique widely used in the least square Monte Carlo method for the valuation of American options.
Approximate integration of stochastic differential equations
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Moreno, M., and Navas, J.F., On the Robustness of Least-Squares Monte Carlo (LSM) for Pricing American Derivatives. Review of Derivatives Research,
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Accelerating the least-square monte carlo method with parallel computing
Chen, C., Huang, K., and Lyuu, Y. (2015) · 2015
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Valuing American options by simulation: a simple least-squares approach
Longstaff, F., and Schwartz, E. (2015) · 2015
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Kim, J., Kim, T., Jo, J., Choi, Y., Lee, S., Hwang, H., Yoo, M. and Jeong, D., A practical finite difference method for the three-dimensional Black–Scholes equation. European Journal of Operational Research,
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Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
E, W., Han, J., and Jentzen, A. (2017) · 2017
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Solving high-dimensional partial differential equations using deep learning
Han, J., Jentzen, A., and E, W. (2018) · 2018
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Hull, J.C., Chapter 1 Introduction. Options, Futures, and Other Derivatives
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Raissi, M. (2018) · 2018
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DGM: A deep learning algorithm for solving partial differential equations
Sirignano, J., and Spiliopoulos, K. (2018) · 2018
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Wang, H., Chen, H., Sudjianto, A., Liu, R., and Shen, Q. (2018) · 2018
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Stochastic gradient descent in continuous time
Sirignano, J., and Spiliopoulos, K. (2017) · 2017
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De Spiegeleer, J., Madan, D.B., Reyners, S., and Schoutens, W. (2018) · 2018
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Asymptotic expansion as prior knowledge in deep learning method for high dimensional BSDEs
Fujii, M., Takahashi, A., and Takahashi, M. (2019) · 2019
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