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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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Backward Stochastic Differential Equations [PDF]
, 2015 In this chapter, we consider a different type of stochastic differential equation. In the setting of Chapter 17, we specified a solution process X through its dynamics and its initial value, as in ( 17.6). In this chapter, we specify a solution process Y through its dynamics and its terminal value, at a fixed, deterministic time \(T \in ]0,\infty ...
Samuel N. Cohen, Robert J. Elliott
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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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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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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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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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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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Abstract and Applied Analysis, 2012 We study the optimal control problem of a controlled time-symmetric forward-backward doubly stochastic differential equation with initial-terminal state constraints. Applying the terminal perturbation method and Ekeland’s variation principle, a necessary
Shaolin Ji, Qingmeng Wei, Xiumin Zhang
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