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Backward doubly stochastic differential equations with infinite time horizon [PDF]
, 2012 summary:We give a sufficient condition on the coefficients of a class of infinite horizon backward doubly stochastic differential equations (BDSDES), under which the infinite horizon BDSDES have a unique solution for any given square integrable terminal
Zhu, Bo, Han, Baoyan
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Backward Deep BSDE Methods and Applications to Nonlinear Problems
Risks, 2023 We present a pathwise deep Backward Stochastic Differential Equation (BSDE) method for Forward Backward Stochastic Differential Equations with terminal conditions that time-steps the BSDE backwards and apply it to the differential rates problem as a ...
Yajie Yu +2 more
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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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Partial Differential Equations in Applied Mathematics, 2022 Backward stochastic differential equation solver was first introduced by Han et al in 2017. A semilinear parabolic partial differential equation is converted into a stochastic differential equation, and then solved by the backward stochastic differential
Evan Davis +4 more
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FBSDEs with time delayed generators:L-P-solutions, differentiability, representation formulas and path regularity [PDF]
, 2011 We extend the work of Delong and Imkeller (2010) [6,7] concerning backward stochastic differential equations with time delayed generators (delay BSDEs). We give moment and a priori estimates in general L-p-spaces and provide sufficient conditions for the
Gonçalo dos Reis +5 more
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, 2008 This paper deals with a class of backward stochastic differential equations with Poisson jumps and with random terminal times. We prove the existence and uniqueness result of adapted solution for such a BSDE under the assumption of non-Lipschitzian ...
Mao, X. +5 more
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Stochastic differential utility as the continuous-time limit of recursive utility [PDF]
, 2013 We establish a convergence theorem that shows that discrete-time recursive utility, as developed by Kreps and Porteus (1978), converges to stochastic differential utility, as introduced by Dufffie and Epstein (1992), in the continuous-time limit of ...
Seifried, Frank Thomas, Kraft, Holger
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Abstract and Applied Analysis, 2014 We discuss a new type of fully coupled forward-backward stochastic differential equations (FBSDEs) whose coefficients depend on the states of the solution processes as well as their expected values, and we call them fully coupled mean-field forward ...
Hui Min, Ying Peng, Yongli Qin
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Backward stochastic partial differential equations driven by infinite-dimensional martingales and applications [PDF]
This paper studies first a result of existence and uniqueness of the solution to a backward stochastic differential equation driven by an infinite-dimensional martingale.
Al-Hussein, AbdulRahman
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