A Global Stochastic Maximum Principle for Fully Coupled Forward-Backward Stochastic Systems

Hu, Mingshang; Ji, Shaolin; Xue, Xiaole

doi:10.1137/18m1179547

Cited by 56 publications

(46 citation statements)

References 50 publications

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“…Note that y ρ θ (t) − y θ (t) = ρ( y ρ θ (t) + y θ (t)). Then, with the help of inequalities (11) and (13), we obtain that…”

Section: Stochastic Maximum Principlementioning

confidence: 99%

Stochastic Maximum Principle for Stochastic Recursive Optimal Control Problem Under Volatility Ambiguity

Hu¹,

Ji²

2016

SIAM J. Control Optim.

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In this paper, we consider a stochastic recursive optimal control problem under model uncertainty. In this framework, the cost function is described by solutions of a family of backward stochastic differential equations. With the help of the linearization techniques and weak convergence methods, we derive the corresponding stochastic maximum principle. Moreover, a linear quadratic robust control problem is also studied.

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“…Note that y ρ θ (t) − y θ (t) = ρ( y ρ θ (t) + y θ (t)). Then, with the help of inequalities (11) and (13), we obtain that…”

Section: Stochastic Maximum Principlementioning

confidence: 99%

Stochastic Maximum Principle for Stochastic Recursive Optimal Control Problem Under Volatility Ambiguity

Hu¹,

Ji²

2016

SIAM J. Control Optim.

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“…Hu overcome the above two difficulties by building a new second-order Taylor expansion of the variation of Y . His idea has been borrowed to investigate the control problems of fully coupled forward-backward stochastic control systems, see [19].…”

Section: Introductionmentioning

confidence: 99%

A global maximum principle for optimal control of general mean-field forward-backward stochastic systems with jumps

Hao

Meng

2020

ESAIM: COCV

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The purpose of this paper is to explore the necessary conditions for optimality of meanfield forward-backward delay control systems. A new estimate is proved, which is a powerful tool to deal with the optimal control problems of mean-field type with delay. Different from the classical situation, in our case the first-order adjoint system is an anticipated mean-field backward stochastic differential equation, and the second-order adjoint system is a system of matrix-valued process, not mean-field type. With the help of two adjoint systems, the second-order expansion of the variation of the state Y is proved, and therewith the Peng's stochastic maximum principle. As an illustrative example, we apply our result to the meanfield game in Finance. Although we just investigate the case of one pointwise delay for convenience, but our method is adequate for analysing the case of pointwise delay.

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“…The stochastic optimal control problem has been an important research topic recently. Many papers have been published in the past few years, for example, References 1‐14. However, in the above literatures, controlled dynamic systems only depend on the current state.…”

Section: Introductionmentioning

confidence: 99%

Stochastic recursive optimal control problem with mixed delay under viscosity solution's framework

Meng

Shi

2020

Optim Control Appl Methods

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Summary This article is concerned with the stochastic recursive optimal control problem with mixed delay. The connection between Pontryagin's maximum principle and Bellman's dynamic programming principle is discussed. Without containing any derivatives of the value function, relations among the adjoint processes and the value function are investigated by employing the notions of super‐ and sub‐jets introduced in defining the viscosity solutions. Stochastic verification theorem is also given to verify whether a given admissible control is really optimal.

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A Global Stochastic Maximum Principle for Fully Coupled Forward-Backward Stochastic Systems

Cited by 56 publications

References 50 publications

Stochastic Maximum Principle for Stochastic Recursive Optimal Control Problem Under Volatility Ambiguity

Stochastic Maximum Principle for Stochastic Recursive Optimal Control Problem Under Volatility Ambiguity

A global maximum principle for optimal control of general mean-field forward-backward stochastic systems with jumps

Stochastic recursive optimal control problem with mixed delay under viscosity solution's framework

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