A Stochastic Recursive Optimal Control Problem Under the G-expectation Framework

A Stochastic Recursive Optimal Control Problem Under the G-expectation Framework In this paper, we study a stochastic recursive optimal control problem in which the objective functional is described by the solution of a backward stochastic differential equation driven by $$G$$ G -Brownian motion. Under standard assumptions, we establish the dynamic programming principle and the related Hamilton–Jacobi–Bellman (HJB) equation in the framework of $$G$$ G -expectation. Finally, we show that the value function is the viscosity solution of the obtained HJB equation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics and Optimization Springer Journals

A Stochastic Recursive Optimal Control Problem Under the G-expectation Framework

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Publisher
Springer US
Copyright
Copyright © 2014 by Springer Science+Business Media New York
Subject
Mathematics; Calculus of Variations and Optimal Control; Optimization; Systems Theory, Control; Theoretical, Mathematical and Computational Physics; Mathematical Methods in Physics; Numerical and Computational Physics
ISSN
0095-4616
eISSN
1432-0606
D.O.I.
10.1007/s00245-014-9242-8
Publisher site
See Article on Publisher Site

Abstract

In this paper, we study a stochastic recursive optimal control problem in which the objective functional is described by the solution of a backward stochastic differential equation driven by $$G$$ G -Brownian motion. Under standard assumptions, we establish the dynamic programming principle and the related Hamilton–Jacobi–Bellman (HJB) equation in the framework of $$G$$ G -expectation. Finally, we show that the value function is the viscosity solution of the obtained HJB equation.

Journal

Applied Mathematics and OptimizationSpringer Journals

Published: Oct 1, 2014

References

  • Function spaces and capacity related to a sublinear expectation: application to $$G$$ G -Brownian motion paths
    Denis, L; Hu, M; Peng, S
  • Backward stochastic differential equations in finance
    Karoui, N; Peng, S; Quenez, MC
  • Ambiguous volatility and asset pricing in continuous time
    Epstein, L; Ji, S
  • Stochastic optimal control problems under G-expectation
    Zhang, DF

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