Results 231 to 240 of about 3,515 (265)

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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Sinc-$\theta$ Schemes for Backward Stochastic Differential Equations

SIAM Journal on Numerical Analysis, 2022
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Xu Wang, Weidong Zhao, Tao Zhou
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Backward Stochastic Differential Equations

2014
In this chapter we discuss so-called “backward stochastic differential equations”, BSDEs for short. Linear BSDEs first appeared a long time ago, both as the equations for the adjoint process in stochastic control, as well as the model behind the Black and Scholes formula for the pricing and hedging of options in mathematical finance. These linear BSDEs
Etienne Pardoux, Aurel Răşcanu
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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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Backward Stochastic Differential Equations

2013
We saw in Chap. 4 that the problem of pricing and hedging financial derivatives can be modeled in terms of (possibly reflected) backward stochastic differential equations (BSDEs) or, equivalently in the Markovian setup, by partial integro-differential equations or variational inequalities (PIDEs or PDEs for short). Also, Chaps.
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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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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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