Results 1 to 10 of about 72 (69)
International Journal of Mathematics for IndustryThis paper introduces an asymptotic expansion for the smooth solution of a semi-linear partial differential equation. Our scheme is based on Itô’s formula, Taylor’s expansion, nonlinear Feynman–Kac formula and some algebras.
Kaori Okuma
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On nonlinear Feynman–Kac formulas for viscosity solutions of semilinear parabolic partial differential equations [PDF]
Stochastics and Dynamics, 2021 The classical Feynman–Kac identity builds a bridge between stochastic analysis and partial differential equations (PDEs) by providing stochastic representations for classical solutions of linear Kolmogorov PDEs. This opens the door for the derivation of sampling based Monte Carlo approximation methods, which can be meshfree and thereby stand a chance ...
Christian Beck +2 more
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A fully nonlinear Feynman–Kac formula with derivatives of arbitrary orders
Journal of Evolution Equations, 2023 We present an algorithm for the numerical solution of nonlinear parabolic partial differential equations. This algorithm extends the classical Feynman-Kac formula to fully nonlinear partial differential equations, by using random trees that carry information on nonlinearities on their branches.
Jiang Yu Nguwi +2 more
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Study of Pricing of High-Dimensional Financial Derivatives Based on Deep Learning
Mathematics, 2023 Many problems in the fields of finance and actuarial science can be transformed into the problem of solving backward stochastic differential equations (BSDE) and partial differential equations (PDEs) with jumps, which are often difficult to solve in high-
Xiangdong Liu, Yu Gu
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BSDE, path-dependent PDE and nonlinear Feynman-Kac formula [PDF]
Science China Mathematics, 2015 In this paper, we introduce a type of path-dependent quasilinear (parabolic) partial differential equations in which the (continuous) paths on an interval [0,t] becomes the basic variables in the place of classical variables (t,x). This new type of PDE are formulated through a classical backward stochastic differential equation (BSDEs, for short) in ...
Peng, ShiGe, Wang, FaLei
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Nonlinear Differential Equations and Applications NoDEA, 2022 Abstract We consider a system of forward backward stochastic differential equations (FBSDEs) with a time-delayed generator driven by Lévy-type noise. We establish a non-linear Feynman–Kac representation formula associating the solution given by the FBSDEs system to the solution of a path dependent nonlinear Kolmogorov equation with ...
Di Persio, Luca +2 more
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Applications of anticipated BSDEs driven by time-changing Lévy noises
Journal of Inequalities and Applications, 2016 We study a very particular anticipated BSDEs when the driver is time-changing Lévy noise. We give an estimate of the solutions in the system satisfying some non-Lipschitz conditions. Also, we state an useful comparison theorem for the solutions. At last,
Youxin Liu
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Nonlinear Feynman–Kac formula and discrete-functional-type BSDEs with continuous coefficients
Stochastic Processes and their Applications, 2004 The authors study a class of multi-dimensional backward stochastic differential equations (BSDEs) of the following form: \[ Y_t = g(X)_T+\int_t^T f(r,X,Y_r,Z_r)\,dr- \int_t^T Z_r\,dW_r,\quad t\in[0,T], \tag{1} \] where \(X\) is an \(n\)-dimensional diffusion satisfying the SDE \[ X_t=x+\int_0^t b(r,X_r)\,dr + \int_0^t\sigma(r,X_r)\,dW_r,\quad t\in[0, T]
Hu, Ying, Ma, Jin
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Nonlinear Feynman-Kac formulae for SPDEs with space-time noise
, 2017 We study a class of backward doubly stochastic differential equations (BDSDEs) involving martingales with spatial parameters, and show that they provide probabilistic interpretations (Feynman-Kac formulae) for certain semilinear stochastic partial differential equations (SPDEs) with space-time noise.
Song, Jian, Song, Xiaoming, Zhang, Qi
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