648 research outputs found
A Class of Backward Doubly Stochastic Differential Equations with Discontinuous Coefficients
In this work the existence of solutions of one-dimensional backward dou- bly
stochastic differential equations (BDSDEs in short) where the coefficient is
left-Lipschitz in y (may be discontinuous) and Lipschitz in z is studied. Also,
the associated comparison theorem is obtained.Comment: 15 page
The Equivalence between Uniqueness and Continuous Dependence of Solution for BDSDEs
In this paper, we prove that, if the coefficient f = f(t; y; z) of backward
doubly stochastic differential equations (BDSDEs for short) is assumed to be
continuous and linear growth in (y; z); then the uniqueness of solution and
continuous dependence with respect to the coefficients f, g and the terminal
value are equivalent.Comment: 11 page
Maximum principle for a stochastic delayed system involving terminal state constraints
We investigate a stochastic optimal control problem where the controlled
system is depicted as a stochastic differential delayed equation; however, at
the terminal time, the state is constrained in a convex set. We firstly
introduce an equivalent backward delayed system depicted as a time-delayed
backward stochastic differential equation. Then a stochastic maximum principle
is obtained by virtue of Ekeland's variational principle. Finally, applications
to a state constrained stochastic delayed linear-quadratic control model and a
production-consumption choice problem are studied to illustrate the main
obtained result.Comment: 16 page
Forward-Backward Doubly Stochastic Differential Equations with Random Jumps and Stochastic Partial Differential-Integral Equations
In this paper, we study forward-backward doubly stochastic differential
equations driven by Brownian motions and Poisson process (FBDSDEP in short).
Both the probabilistic interpretation for the solutions to a class of
quasilinear stochastic partial differential-integral equations (SPDIEs in
short) and stochastic Hamiltonian systems arising in stochastic optimal control
problems with random jumps are treated with FBDSDEP. Under some monotonicity
assumptions, the existence and uniqueness results for measurable solutions of
FBDSDEP are established via a method of continuation. Furthermore, the
continuity and differentiability of the solutions of FBDSDEP depending on
parameters is discussed. Finally, the probabilistic interpretation for the
solutions to a class of quasilinear SPDIEs is given
Zero-sum linear quadratic stochastic integral games and BSVIEs
This paper formulates and studies a linear quadratic (LQ for short) game
problem governed by linear stochastic Volterra integral equation. Sufficient
and necessary condition of the existence of saddle points for this problem are
derived. As a consequence we solve the problems left by Chen and Yong in [3].
Firstly, in our framework, the term GX^2(T) is allowed to be appear in the cost
functional and the coefficients are allowed to be random. Secondly we study the
unique solvability for certain coupled forward-backward stochastic Volterra
integral equations (FBSVIEs for short) involved in this game problem. To
characterize the condition aforementioned explicitly, some other useful tools,
such as backward stochastic Fredholm-Volterra integral equations (BSFVIEs for
short) and stochastic Fredholm integral equations (FSVIEs for short) are
introduced. Some relations between them are investigated. As a application, a
linear quadratic stochastic differential game with finite delay in the state
variable and control variables is studied.Comment: 27 page
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