Machine Learning Approximation Algorithms for High-Dimensional Fully Nonlinear Partial Differential Equations and Second-order Backward Stochastic Differential Equations
نویسندگان
چکیده
منابع مشابه
Machine learning approximation algorithms for high-dimensional fully nonlinear partial differential equations and second-order backward stochastic differential equations
High-dimensional partial differential equations (PDE) appear in a number of models from the financial industry, such as in derivative pricing models, credit valuation adjustment (CVA) models, or portfolio optimization models. The PDEs in such applications are high-dimensional as the dimension corresponds to the number of financial assets in a portfolio. Moreover, such PDEs are often fully nonli...
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Second-Order Backward Stochastic Differential Equations and Fully Nonlinear Parabolic PDEs
In the probability literature, backward stochastic differential equations (BSDE) received considerable attention after their introduction by E. Pardoux and S. Peng [5, 6] in 1990. During the past decade, interesting connections to partial differential equations (PDE) were obtained and the theory found wide applications in mathematical finance. The key property of the BSDE’s is the random termin...
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This is the author’s version of a work that was accepted for publication in Journal of Computational and Applied Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A ...
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ژورنال
عنوان ژورنال: Journal of Nonlinear Science
سال: 2019
ISSN: 0938-8974,1432-1467
DOI: 10.1007/s00332-018-9525-3