Results 121 to 130 of about 3,119 (165)

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

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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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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Backward Stochastic Differential Equations

1999
In Chapter 3, in order to derive the stochastic maximum principle as a set of necessary conditions for optimal controls, we encountered the problem of finding adapted solutions to the adjoint equations. Those are terminal value problems of (linear) stochastic differential equations involving the Ito stochastic integral. We call them backward stochastic
Jiongmin Yong, Xun Yu Zhou
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On Reflected Backward Stochastic Differential Equations

Calcutta Statistical Association Bulletin, 2002
Some aspects of reflected backward stochastic differential equations in a half-line or in an orthant are surveyed. The roleof an optimal stopping problem in solving RBSDE in a half-line is highlighted. RBSDE in an orthant with time-space dependent oblique reflection is formulated and an outline of the ideas involved in proving the existence of a ...
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Backward Stochastic Differential Equations in the Plane

Potential Analysis, 2002
Backward stochastic differential equations have been introduced by \textit{E. Pardoux} and \textit{S. G. Peng} [Syst. Control Lett. 14, No. 1, 55-61 (1990; Zbl 0692.93064)]. They proved existence and uniqueness of an adapted solution \((Y_t, Z_t)\) of the equation \(dY_t= -f(t;Y_t,Z_t) dt+ Z_t dW_t\), \(t\in [0,T]\), driven by a Brownian motion \(W ...
Zaïdi, N. Lanjri, Nualart, D.
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Stochastic Differential Equations, Backward SDEs, Partial Differential Equations

2014
This research monograph presents results to researchers in stochastic calculus, forward and backward stochastic differential equations, connections between diffusion processes and second order partial differential equations (PDEs), and financial mathematics.
Pardoux, Etienne, Răşcanu, Aurel
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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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Markovian forward–backward stochastic differential equations and stochastic flows

Systems & Control Letters, 2012
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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