86 research outputs found
General Linear Quadratic Optimal Stochastic Control Problem Driven by a Brownian Motion and a Poisson Random Martingale Measure with Random Coefficients
The main purpose of this paper is to discuss detailed the stochastic LQ
control problem with random coefficients where the linear system is a
multidimensional stochastic differential equation driven by a multidimensional
Brownian motion and a Poisson random martingale measure. In the paper, we will
establish the connections of the multidimensional Backward stochastic Riccati
equation with jumps (BSRDEJ in short form) to the stochastic LQ problem and to
the associated Hamilton systems. By the connections, we show the optimal
control have the state feedback representation. Moreover, we will show the
existence and uniqueness result of the multidimensional BSRDEJ for the case
where the generator is bounded linear dependence with respect to the unknowns
martingale term
A Maximum Principle for Optimal Control of Stochastic Evolution Equations
A general maximum principle is proved for optimal controls of abstract
semilinear stochastic evolution equations. The control variable, as well as
linear unbounded operators, acts in both drift and diffusion terms, and the
control set need not be convex.Comment: 20 page
A global maximum principle for optimal control of general mean-field forward-backward stochastic systems with jumps
In this paper we prove a necessary condition of the optimal control problem
for a class of general mean-field forward-backward stochastic systems with
jumps in the case where the diffusion coefficients depend on control, the
control set does not need to be convex, the coefficients of jump terms are
independent of control as well as the coefficients of mean-field backward
stochastic differential equations depend on the joint law of . Two
new adjoint equations are brought in as well as several new generic estimates
of their solutions are investigated for analysing the higher terms, especially,
those involving the expectation which come from the derivatives of the
coefficients with respect to the measure. Utilizing these subtle estimates, the
second-order expansion of the cost functional, which is the key point to
analyse the necessary condition, is obtained, and whereafter the stochastic
maximum principle.Comment: 32 page
Notes on the Cauchy Problem for Backward Stochastic Partial Differential Equations
Backward stochastic partial differential equations of parabolic type with
variable coefficients are considered in the whole Euclidean space. Improved
existence and uniqueness results are given in the Sobolev space
() under weaker assumptions than those used by X. Zhou [Journal of
Functional Analysis 103, 275--293 (1992)]. As an application, a comparison
theorem is obtained.Comment: 20 page
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