Maximum principle for forward-backward control system driven by Itô-Lévy processes under initial-terminal constraints
type: Item
instance of: scholarly article
title: Maximum principle for forward-backward control system driven by Itô-Lévy processes under initial-terminal constraints
zbMATH Open document ID: 1426.93367
DOI: 10.1155/2017/1868560
author: Meijuan Liu
author: Hong Huang
author: Xiangrong Wang
published in: Mathematical Problems in Engineering
publication date: 2018-11-05T00:00:00Z
review text: Summary: This paper investigates a stochastic optimal control problem where the control system is driven by Itô-Lévy process. We prove the necessary condition about existence of optimal control for stochastic system by using traditional variational technique under the assumption that control domain is convex. We require that forward-backward stochastic differential equations (FBSDE) be fully coupled, and the control variable is allowed to enter both diffusion and jump coefficient. Moreover, we also require that the initial-terminal state be constrained. Finally, as an application to finance, we show an example of recursive consumption utility optimization problem to illustrate the practicability of our result.
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 49K45
Mathematics Subject Classification ID: 60H10
zbMATH DE Number: 6971810
Wikidata QID: Q59147326
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/1868560
OpenAlex ID: W2633993420
cites work: Q4742672
cites work: Stochastic maximum principle for distributed parameter systems
cites work: Backward stochastic differential equations and applications to optimal control
cites work: A General Stochastic Maximum Principle for Optimal Control Problems
cites work: Q4255599
cites work: Q4266941
cites work: Fully Coupled Forward-Backward Stochastic Differential Equations and Applications to Optimal Control
cites work: A maximum principle for stochastic optimal control with terminal state constraints, and its applications
cites work: Stochastic linear quadratic optimal control with constraint for discrete-time systems
cites work: Maximum principle for the optimal control problem of a fully coupled stochastic system with state constraints
cites work: Q5452980
cites work: A maximum principle for optimal control problem of fully coupled forward-backward stochastic systems with partial information
cites work: A maximum principle for fully coupled forward-backward stochastic control systems with terminal state constraints
cites work: Chaotic and predictable representations for Lévy processes.
cites work: Lévy Processes and Stochastic Calculus
cites work: Maximum Principles for Optimal Control of Forward-Backward Stochastic Differential Equations with Jumps
cites work: Maximum principle for forward-backward stochastic control system with random jumps and applications to finance
cites work: Necessary conditions for optimal control of forward-backward stochastic systems with random jumps
cites work: Q5499397
cites work: Risk minimization in financial markets modeled by Itô-Lévy processes
cites work: Forward-backward stochastic differential equations with Brownian motion and Poisson process
cites work: On the variational principle
description: scientific article; zbMATH DE number 6971810