Results 51 to 60 of about 3,305 (167)

Mean field forward-backward stochastic differential equations

Electronic Communications in Probability, 2013
The purpose of this note is to provide an existence result for the solution of fully coupled Forward Backward Stochastic Differential Equations (FBSDEs) of the mean field type. These equations occur in the study of mean field games and the optimal control of dynamics of the McKean Vlasov type.
Carmona, René, Delarue, François
openaire   +5 more sources

Controlled Reflected McKean–Vlasov SDEs and Neumann Problem for Backward SPDEs

Mathematics
This paper is concerned with the stochastic optimal control problem of a 1-dimensional McKean–Vlasov stochastic differential equation (SDE) with reflection, of which the drift coefficient and diffusion coefficient can be both dependent on the state of ...
Li Ma, Fangfang Sun, Xinfang Han
doaj   +1 more source

Infinite horizon forward–backward stochastic differential equations

Stochastic Processes and their Applications, 2000
Let \(B\) be a standard \(d\)-dimensional Wiener process defined on a probability space \((\Omega ,\mathfrak F,P)\), let \((\mathfrak F_{t})\) be the (augmented) natural filtration of \(B\). An infinite horizon forward-backward stochastic differential equation \[ \begin{aligned} & dX(t) = b(t,X(t),Y(t),Z(t)) dt + \sigma (t,X(t), Y(t),Z(t)) dB(t), \tag ...
Peng, Shige, Shi, Yufeng
openaire   +1 more source

Numberical Method for Backward Stochastic Differential Equations

The Annals of Applied Probability, 2002
Let \(W\) be a \(d\)-dimensional Brownian motion. The authors develop a new method of approximating solutions \(Y\) of the multidimensional backward stochastic differential equation (BSDE) \[ dY_t= -f(t, Y_t)dt+ Z_t dW_t,\quad t\in [0,T], \] with a continuous driver \(f\) which is Lipschtz in the \(y\)-variable and independent of \(z\).
Ma, Jin, Protter, Philip, San Martín Aristegui, Jaime, Torres, Soledad   +3 more
openaire   +2 more sources

Option pricing mechanisms driven by backward stochastic differential equations

Financial Innovation
This study investigates an option pricing method called g-pricing based on backward stochastic differential equations combined with deep learning.
Yufeng Shi, Bin Teng, Sicong Wang
doaj   +1 more source

The Semimartingale Approach to Almost Sure Stability Analysis of a Two-Stage Numerical Method for Stochastic Delay Differential Equation

Abstract and Applied Analysis, 2014
Almost sure exponential stability of the split-step backward Euler (SSBE) method applied to an Itô-type stochastic differential equation with time-varying delay is discussed by the techniques based on Doob-Mayer decomposition and semimartingale ...
Qian Guo, Xueyin Tao
doaj   +1 more source

A class of stochastic Gronwall’s inequality and its application

Journal of Inequalities and Applications, 2018
This paper puts forward the basic form of stochastic Gronwall’s inequality and uses, respectively, the iterative method, the integral method and the martingale representation method to prove it.
Xin Wang, Shengjun Fan
doaj   +1 more source

Nonlinear Decomposition of Doob-Meyer's Type for Continuous g-Supermartingale with Uniformly Continuous Coefficient

Journal of Applied Mathematics, 2014
We prove that a continuous g-supermartingale with uniformly continuous coeffcient g on finite or infinite horizon, is a g-supersolution of the corresponding backward stochastic differential equation. It is a new nonlinear Doob-Meyer decomposition theorem
Xuejun Shi, Long Jiang, Ronglin Ji
doaj   +1 more source

Stochastic Control Representations for Penalized Backward Stochastic Differential Equations [PDF]

SIAM Journal on Control and Optimization, 2015
24 pages in SIAM Journal on Control and Optimization ...
openaire   +6 more sources

Stochastic Differential Games and a Unified Forward–Backward Coupled Stochastic Partial Differential Equation with Lévy Jumps

Mathematics
We establish a relationship between stochastic differential games (SDGs) and a unified forward–backward coupled stochastic partial differential equation (SPDE) with discontinuous Lévy Jumps. The SDGs have q players and are driven by a general-dimensional
Wanyang Dai
doaj   +1 more source