Results 231 to 240 of about 3,335 (259)

On Weak Solutions of Backward Stochastic Differential Equations

Theory of Probability & Its Applications, 2005
Existence of a weak solution (in the Meyer-Zheng topology) of a backward stochastic differential equation of the form \[ Y_t=E\left[\left.H(X)+ \int^T_t f(s,X,Y)ds \right| {\mathcal F}_t^x\right],\quad t\in [0,T], \] is proved. It is also proved that pathwise uniqueness plus existence of a weak solution imply the existence of a pathwise unique strong ...
Buckdahn, R., Engelbert, H.-J., Răşcanu, A.   +2 more
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On backward stochastic differential equations

Stochastics, 1982
Given a forward ( = usual) stochastic differential equation (SDE), we consider, in this paper, an associated backward SDE. Let E;s,t(x),t∈[s, ∞) be the solution of an SDE on a manifold M: with the initial condition ξs,s(x) =x. Here X 0,…,X r are smooth vector fields, (B t 1,…,B t 1) is a standard r-dimensional Brownian motion and o denotes the ...
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Markovian forward–backward stochastic differential equations and stochastic flows

Systems & Control Letters, 2012
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Robert J. Elliott, Tak Kuen Siu
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Backward stochastic differential equations and stochastic controls

Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304), 2003
The paper attempts to explore the relationship between backward stochastic differential equations (BSDEs) and stochastic controls by interpreting a BSDE as some stochastic optimal control problem. The latter is solved in a closed form by the stochastic linear-quadratic (LQ) theory. The general result is then applied to the Black-Scholes model, where an
M. Kohlmann, null Xun Yu Zhou
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Jensen’s Inequality for Backward Stochastic Differential Equations*

Chinese Annals of Mathematics, Series B, 2006
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MULTIVALUED STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS VIA BACKWARD DOUBLY STOCHASTIC DIFFERENTIAL EQUATIONS

Stochastics and Dynamics, 2008
In this paper, we establish by means of Yosida approximation, the existence and uniqueness of the solution of a backward doubly stochastic differential equation whose coefficient contains the subdifferential of a convex function. We will use this result to prove the existence of stochastic viscosity solution for some multivalued parabolic stochastic ...
Boufoussi, B., Mrhardy, N.
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Anticipated Backward Stochastic Differential Equation with Reflection

Communications in Statistics - Simulation and Computation, 2016
In this article, we deal with anticipated backward stochastic differential equation with reflecting boundary. The existence and uniqueness of solution is obtained for equation with Lipschitz and non-Lipschitz generator.
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Backward Stochastic Differential Equations Driven By Càdlàg Martingales

Theory of Probability & Its Applications, 2008
Backward stochastic differential equations (BSDEs) arise in many financial problems. Although there exists a growing number of papers considering general financial markets, the theory of BSDEs has been developed just in the Brownian setting. We consider BSDEs driven by an ${\bf R}^d$-valued cadlag martingale and we study the properties of the solutions
CARBONE R, FERRARIO B, SANTACROCE, MARINA   +2 more
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Splitting Schemes for Backward Stochastic Differential Equations

International Journal of Numerical Analysis and Modeling
This paper concerns splitting methods for solving backward stochastic differential equations (BSDEs). By splitting the original $d$-dimensional BSDE into $d$ BSDEs and approximating these split BSDEs, we propose splitting schemes for the BSDE. The splitting schemes are rigorously analyzed and first-order error estimates are theoretically obtained ...
Zheng, Luying, Zhao, Weidong
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Backward stochastic differential equations and integral-partial differential equations

Stochastic and Stochastics Reports, 1997
Etienne Pardoux, Rainer Buckdahn, Guy Barlés   +2 more
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