arXiv subjects

Qiuhong Shi

Publications and source records attributed to Qiuhong Shi.

5 recordsLinked to original sources

arXiv2017

Maximum Principle of Forward-Backward Stochastic Differential System of Mean-Field Type with Observation Noise

This paper is concerned with the partial information optimal control problem of mean-field type under partial observation, where the system is given by a controlled mean-field forward-backward stochastic differential equation with correlated noises between the system and the observation, moreover the observation coefficients may depend not only on the control process and but also on its probability distribution. Under standard assumptions on the coefficients, necessary and sufficient conditions for optimality of the control problem in the form of Pontryagin's maximum principles are established in a unified way.

math.OC↗

arXiv2017

Partial Information Near-Optimal Control of Forward-Backward Stochastic Differential System with Observation Noise

This paper first makes an attempt to investigate the partial information near optimal control of systems governed by forward-backward stochastic differential equations with observation noise under the assumption of a convex control domain. By Ekeland's variational principle and some basic estimates for state processes and adjoint processes, we establish the necessary conditions for any $\varepsilon $-near optimal control in a local form with an error order of exact $\varepsilon ^{% \frac{1}{2}}.$ Moreover, under additional convexity conditions on Hamiltonian function, we prove that an $\varepsilon $-maximum condition in terms of the Hamiltonian in the integral form is sufficient for near-optimality.

math.OC↗

arXiv2017

A Revisit to Optimal Control of Forward-Backward Stochastic Differential System with Observation Noise

This paper revisits the partial information optimal control problem considered by Wang, Wu and Xiong [Wang et al 2013], where the system is derived by a controlled forward-backward stochastic differential equation with correlated noises between the system and the observation. For this type of partial information optimal control problem, one necessary and one suffcient (a verification theorem) conditions of optimality are derived using a unified way. We improve the $L^p-$ bounds on the control from $L^8$ in [Want et al 2013] to $L^4$ in this paper.

math.PR↗

arXiv2017

Optimal Control with State Constraints for Stochastic Evolution Equation with Jumps in Hilbert Space

This paper studies a stochastic optimal control problem with state constraint, where the state equation is described by a controlled stochastic evolution equation with jumps in Hilbert Space and the control domain is assumed to be convex. By means of Ekland variational principle, combining the convex variation method and the duality technique, necessary conditions for optimality are derived in the form of stochastic maximum principles.

math.PR↗

arXiv2017

Stochastic Evolution Equation Driven by Teugels Martingale and Its Optimal Control

The paper is concerned with a class of stochastic evolution equations in Hilbert space with random coefficients driven by Teugel's martingales and an independent multi-dimensional Brownian motion and its optimal control problem. Here Teugels martingales are a family of pairwise strongly orthonormal martingales associated with Lévy processes (see Nualart and Schoutens). There are three major ingredients. The first is to prove the existence and uniqueness of the solutions by continuous dependence theorem of solutions combining with the parameter extension method. The second is to establish the stochastic maximum principle and verification theorem for our optimal control problem by the classic convex variation method and dual technique. The third is to represent an example of a Cauchy problem for a controlled stochastic partial differential equation driven by Teugels martingales which our theoretical results can solve.

math.PR↗