MSThE39
Optimal control of stochastic systems and its application to finance
Date: August 13
Time: 16:0018:20
Room: 302B
(Note: Click title to show the abstract.)
Organizer:
Wu, Zhen (Shandong Univ.)
Wang, Guangchen (Shandong Univ.)
Abstract: Optimal control of stochastic systems plays a central and significant role in modern control theory. In the past decade, extensive studies have been conducted for the socalled maximum principle, verification theorem, HJB equation and their applications to finance, economics, insurance, etc. The minisymposium aims to present some recent developments in optimal control of stochastic systems, including 1) LQ control and filtering of forwardbackward stochastic systems; 2) NonMarkov zerosum Dynkin game; 3) Maximum principle for stochastic systems driven by fractional Brownian motions; 4) Maximum principle for meanfield stochastic delay systems.
MSThE391
16:0016:30
An LQ optimal control problem of FBSDEs with partial information
Wang, Guangchen (Shandong Univ.)
Abstract: In this talk, we study an LQ optimal control problem derived by FBSDEs. A backward separation approach is introduced. Combining it with filtering, two optimality conditions and a feedback optimal control are derived. Closedform optimal solutions are obtained in some particular cases. As an application of the results, a recursive utility problem from financial markets is solved explicitly. (This talk is based on a joint work with Professors Zhen Wu and Jie Xiong.)
MSThE392
16:3017:00
NonMarkov zerosum Dynkin game
Zhou, Yang (South China Normal Univ.)
Abstract: A NonMarkov zerosum Dynkin game problem is considered. Its associated HamiltonJacobiBellmanIsaacs equation is a backward stochastical partial differential variational inequality (BSPDVI, for short) with semilinear differential operator. A verification theorem is established, which shows that the strong solution of the BSPDVI is the value function of the Dynkin game problem. Then the existence and uniqueness of the strong solution of the BSPDVI are proved. Finally, we give two examples to show its applications.
MSThE393
17:0017:30
Stochastic Maximum Principle for Controlled Systems Driven by Fractional and Standard Brownian Motions
Han, Yuecai (Jilin Univ.)
Abstract: The existence and uniqueness of solution for a type of backward stochastic differential equation driven by fractional Brownian motions and underlying standard Brownian motions is investigated. The necessary contions that the optimal control must satisfy for controlled systems driven by fractional Brownian motions and underlying standard Brownian motions is obtained by conditioning and Malliavin calculus.
MSThE394
17:3018:00
Maximum principle for meanfield jumpdiffusion stochastic delay differential equations and its application to finance
Meng, Qingxin (Huzhou Uinversity)
Abstract: This paper investigates a stochastic optimal control problem with delay and of meanfield type,where the controlled state process is governed by a meanfield jumpdiffusion stochastic delay differential equation.Two sufficient maximum principles and one necessary maximum principle are established for the underlying systems. As an application, a bicriteria meanvariance portfolio selection problem with delay is studied.Under certain conditions, explicit expressions are provided for the efficient portfolio and the efficient frontier,
which are as
CPThE395
18:0018:20
The Connection between Dynamic Programming and Maximum Principle for Fully Coupled ForwardBackward Stochastic Control Systems
Shi, Jingtao (Shandong Univ.)
Abstract: This paper is concerned with the connection between dynamic programming (DP) and maximum principle (MP) for the fully coupled forwardbackward stochastic control system. where the recursive cost functional is defined as one of the solution to a controlled forwardbackward stochastic differential equation (FBSDE). With some smooth assumptions, relations among the value function, generalized Hamiltonian function and adjoint processes are given, when the diffusion coefficient of the forward equation does not contain the state variable $z$. The general case for the problem is open. A linear example is discussed as the illustration of our main result.
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Footnote: Code: TypeDateTimeRoom No.
Type : IL=Invited Lecture, SL=Special Lectures, MS=Minisymposia, IM=Industrial Minisymposia, CP=Contributed Papers, PP=Posters
Date: Mo=Monday, Tu=Tuesday, We=Wednesday, Th=Thursday, Fr=Friday
Time : A=8:309:30, B=10:0011:00, C=11:1012:10, BC=10:0012:10, D=13:3015:30, E=16:0018:00, F=19:0020:00, G=12:1013:30, H=15:3016:00
Room No.: TBA
