scholarly journals Maximum Principle for Forward-Backward Stochastic Control System Driven by Lévy Process

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Xiangrong Wang ◽  
Hong Huang
Keyword(s):  
Maximum Principle ◽  
Lévy Process ◽  
Backward Stochastic Differential Equation ◽  
Levy Process ◽  
Linear Quadratic ◽  
Controlled System ◽  
The Maximum Principle ◽  
Stochastic Control System ◽  
Continuity Result ◽  
Stochastic Optimal Control Problem

We study a stochastic optimal control problem where the controlled system is described by a forward-backward stochastic differential equation driven by Lévy process. In order to get our main result of this paper, the maximum principle, we prove the continuity result depending on parameters about fully coupled forward-backward stochastic differential equations driven by Lévy process. Under some additional convexity conditions, the maximum principle is also proved to be sufficient. Finally, the result is applied to the linear quadratic problem.

scholarly journals Linear Quadratic Stochastic Optimal Control of Forward Backward Stochastic Control System Associated with Lévy Process

2017 ◽  
Vol 2017 ◽  
pp. 1-11
Author(s):  
Hong Huang ◽  
Xiangrong Wang ◽  
Ting Hou ◽  
Lu Xu
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Riccati Equation ◽  
Stochastic Control ◽  
Lévy Process ◽  
Levy Process ◽  
Linear Feedback ◽  
Linear Quadratic ◽  
Stochastic Control System ◽  
Generalized Riccati Equation

This paper analyzes one kind of linear quadratic (LQ) stochastic control problem of forward backward stochastic control system associated with Lévy process. We obtain the explicit form of the optimal control, then prove it to be unique, and get the linear feedback regulator by introducing one kind of generalized Riccati equation. Finally, we discuss the solvability of the generalized Riccati equation, and its existence and uniqueness of the solutions are proved in a special case.

scholarly journals A Necessary Condition for Optimal Control of Forward-Backward Stochastic Control System with Lévy Process in Nonconvex Control Domain Case

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Hong Huang ◽  
Xiangrong Wang ◽  
Ying Li
Keyword(s):  
Optimal Control ◽  
Control System ◽  
Lévy Process ◽  
State Constraints ◽  
Terminal State ◽  
Levy Process ◽  
Necessary Condition ◽  
Variational Technique ◽  
The Maximum Principle ◽  
Stochastic Control System

This paper analyzes one kind of optimal control problem which is described by forward-backward stochastic differential equations with Lévy process (FBSDEL). We derive a necessary condition for the existence of the optimal control by means of spike variational technique, while the control domain is not necessarily convex. Simultaneously, we also get the maximum principle for this control system when there are some initial and terminal state constraints. Finally, a financial example is discussed to illustrate the application of our result.

BSDE with rcll reflecting barrier driven by a Lévy process

2020 ◽  
Vol 28 (1) ◽  
pp. 63-77 ◽  
Author(s):  
Mohamed El Jamali ◽  
Mohamed El Otmani
Keyword(s):  
Differential Equation ◽  
Stochastic Differential Equation ◽  
Existence And Uniqueness ◽  
Lévy Process ◽  
Backward Stochastic Differential Equation ◽  
American Option ◽  
Levy Process ◽  
Fair Price ◽  
Penalization Method ◽  
Uniqueness Of A Solution

AbstractIn this paper, we study the solution of a backward stochastic differential equation driven by a Lévy process with one rcll reflecting barrier. We show the existence and uniqueness of a solution by means of the penalization method when the coefficient is stochastic Lipschitz. As an application, we give a fair price of an American option.

scholarly journals Maximum Principle of Discrete Stochastic Control System Driven by Both Fractional Noise and White Noise

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Yuecai Han ◽  
Zheng Li
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
White Noise ◽  
Necessary Optimality Conditions ◽  
Variation Method ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Stochastic Control System ◽  
Fractional Noise ◽  
Quadratic Optimal Control

In this paper, we investigate the necessary optimality conditions of the discrete stochastic optimal control problems driven by both fractional noise and white noise. Here, the admissible control region is not necessarily convex. The corresponding variational inequalities are obtained by applying the classical variation method and Malliavin calculus. We also apply the stochastic maximum principle to a linear-quadratic optimal control problem to illustrate the main result.

scholarly journals Minimizing Banking Risk in a Lévy Process Setting

2007 ◽  
Vol 2007 ◽  
pp. 1-25 ◽  
Author(s):  
F. Gideon ◽  
J. Mukuddem-Petersen ◽  
M. A. Petersen
Keyword(s):  
Risk Management ◽  
Lévy Process ◽  
Management Practices ◽  
Cash Flows ◽  
Levy Process ◽  
Bank Deposits ◽  
Stochastic Optimal Control Problem ◽  
External Sources ◽  
Outstanding Debt ◽  
Management Issues

The primary functions of a bank are to obtain funds through deposits from external sources and to use the said funds to issue loans. Moreover, risk management practices related to the withdrawal of these bank deposits have always been of considerable interest. In this spirit, we construct Lévy process-driven models of banking reserves in order to address the problem of hedging deposit withdrawals from such institutions by means of reserves. Here reserves are related to outstanding debt and acts as a proxy for the assets held by the bank. The aforementioned modeling enables us to formulate a stochastic optimal control problem related to the minimization of reserve, depository, and intrinsic risk that are associated with the reserve process, the net cash flows from depository activity, and cumulative costs of the bank's provisioning strategy, respectively. A discussion of the main risk management issues arising from the optimization problem mentioned earlier forms an integral part of our paper. This includes the presentation of a numerical example involving a simulation of the provisions made for deposit withdrawals via treasuries and reserves.

scholarly journals OPTIMAL CONTROL USING PONTRYAGIN'S MAXIMUM PRINCIPLE IN A LINEAR QUADRATIC DIFFERENTIAL GAME

2012 ◽  
Vol 09 ◽  
pp. 543-551
Author(s):  
MARZIEH KHAKESTARI ◽  
GAFURJAN IBRAGIMOV ◽  
MOHAMED SULEIMAN
Keyword(s):  
Optimal Control ◽  
Maximum Principle ◽  
Differential Game ◽  
Quadratic Differential ◽  
Pontryagin’S Maximum Principle ◽  
Linear Quadratic ◽  
Pontryagin's Maximum Principle ◽  
The Maximum Principle ◽  
Control Functions ◽  
Linear Quadratic Differential Games

This paper deals with a class of two person zero-sum linear quadratic differential games, where the control functions for both players subject to integral constraints. Also the necessary conditions of the Maximum Principle are studied. Main objective in this work is to obtain optimal control by using method of Pontryagin's Maximum Principle. This method for a time-varying linear quadratic differential game is described. Finally, we discuss about an example.

scholarly journals Partially Observed Nonzero-Sum Differential Game of BSDEs with Delay and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Qiguang An ◽  
Qingfeng Zhu
Keyword(s):  
Nash Equilibrium ◽  
Maximum Principle ◽  
Equilibrium Point ◽  
Time Delays ◽  
Necessary Condition ◽  
State Variables ◽  
Linear Quadratic ◽  
Nash Equilibrium Point ◽  
The Maximum Principle ◽  
Partially Observed

A class of partially observed nonzero-sum differential games for backward stochastic differential equations with time delays is studied, in which both game system and cost functional involve the time delays of state variables and control variables under each participant with different observation equations. A necessary condition (maximum principle) for the Nash equilibrium point to this kind of partially observed game is established, and a sufficient condition (verification theorem) for the Nash equilibrium point is given. A partially observed linear quadratic game is taken as an example to illustrate the application of the maximum principle.

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