Results 31 to 40 of about 59,739 (301)
On the robustness of backward stochastic differential equations
Stochastic Processes and their Applications, 2002 The backward stochastic differential equation driven by a Brownian motion \(W=\{W_t\} _{0\leq t\leq T}\), \[ Y_t= \xi + \int _t^T f(r,Y_r, Z_r)\,dr -\int _t^T Z_r\,dW_r,\quad 0\leq t\leq T, \] is considered, where the solution \((Y_t, Z_t)\) is supposed to be progressively measurable with respect to the filtration \(\{\mathcal F_t \}\) defined by the ...
Briand, Philippe +2 more
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Mathematics, 2021 In this paper, we mainly investigate the weak convergence analysis about the error terms which are determined by the discretization for solving the stochastic differential equation (SDE, for short) in forward-backward stochastic differential equations ...
Wei Zhang, Hui Min
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A linear numerical scheme for nonlinear BSDEs with uniformly continuous coefficients
Journal of Applied Mathematics, 2004 We attempt to present a new numerical approach to solve nonlinear backward stochastic differential equations. First, we present some definitions and theorems to obtain the condition, from which we can approximate the nonlinear term of the backward ...
Omid. S. Fard, Ali V. Kamyad
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A stochastic Gronwall inequality in random time horizon and its application to BSDE
Journal of Inequalities and Applications, 2020 In this paper, we introduce and prove a stochastic Gronwall inequality in an (unbounded) random time horizon. As an application, we prove a comparison theorem for backward stochastic differential equation (BSDE for short) with random terminal time under ...
Hun O, Mun-Chol Kim, Chol-Kyu Pak
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Mendel, 2023 We deal with fractional mean field backwardWe deal with fractional mean field backward stochastic differential equations with hurst parameter $H\in (\frac{1}{2},1)$ when the coefficient $f$ satisfy a stochastic Lipschitz conditions, we prove the ...
Mostapha Abdelouahab Saouli
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Backward stochastic differential equations with unbounded generators [PDF]
Stochastics and Dynamics, 2019 In this paper, we consider two classes of backward stochastic differential equations (BSDEs). First, under a Lipschitz-type condition on the generator of the equation, which can also be unbounded, we give sufficient conditions for the existence of a unique solution pair. The method of proof is that of Picard iterations and the resulting conditions are
Gashi, B, Li, J
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Set-valued backward stochastic differential equations
The Annals of Applied Probability, 2023 In this paper, we establish an analytic framework for studying set-valued backward stochastic differential equations (set-valued BSDE), motivated largely by the current studies of dynamic set-valued risk measures for multi-asset or network-based financial models. Our framework will make use of the notion of Hukuhara difference between sets, in order to
Ararat, Cagin, Ma, Jin, Wu, Wenqian
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Deep Learning-Based Numerical Methods for High-Dimensional Parabolic Partial Differential Equations and Backward Stochastic Differential Equations [PDF]
Communications in Mathematics and Statistics, 2017 We study a new algorithm for solving parabolic partial differential equations (PDEs) and backward stochastic differential equations (BSDEs) in high dimension, which is based on an analogy between the BSDE and reinforcement learning with the gradient of ...
W. E, Jiequn Han, Arnulf Jentzen
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Backward-Forward Stochastic Differential Equations
The Annals of Applied Probability, 1993 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Multi-dimensional backward stochastic differential equations of diagonally quadratic generators: The general result [PDF]
Journal of Differential Equations, 2020 This paper is devoted to a general solvability of a multi-dimensional backward stochastic differential equation (BSDE) of a diagonally quadratic generator $g(t,y,z)$, by relaxing the assumptions of \citet{HuTang2016SPA} on the generator and terminal ...
Shengjun Fan, Ying Hu, Shanjian Tang
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