Results 131 to 140 of about 3,305 (167)

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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Markovian forward–backward stochastic differential equations and stochastic flows

Systems & Control Letters, 2012
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Elliott, R., Siu, T.
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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 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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Jensen’s Inequality for Backward Stochastic Differential Equations*

Chinese Annals of Mathematics, Series B, 2006
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Backward stochastic differential equations and integral-partial differential equations

Stochastics and Stochastic Reports, 1997
We consider a backward stochastic differential equation, whose data (the final condition and the coefficient) are given functions of a jump-diffusion process. We prove that under mild conditions the solution of the BSDE provides a viscosity solution of a system of parabolic integral-partial differential equations.
Guy Barles, Rainer Buckdahn, Etienne Pardoux   +2 more
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Forward-Backward Stochastic Differential Equations

2013
We investigate a backward SDE with a generator and a terminal condition which depend on the state of a Markov process solving a forward SDE driven by a Brownian motion and a compensated Poisson random measure. Such an equation is called a forward-backward SDE. In the Markovian setting we show that the unique solution to a backward SDE can be written as
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HJB Equations Through Backward Stochastic Differential Equations

2017
This last chapter of the book completes the picture of the main methods used to study second-order HJB equations in Hilbert spaces and related optimal control problems by presenting a survey of results that can be achieved with the techniques of Backward SDEs in infinite dimension.
Fuhrman, M, Tessitore, G.
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Quadratic backward stochastic differential equations

2017
In this thesis, we analyze backward stochastic differential equations. We begin by introducing stochastic processes, Brownian motion, stochastic integrals, and Itô's formula. After that, we move on to consider stochastic differential equations and finally backward stochastic differential equations.
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