一个倒向随机微分时滞方程的最优控制问题
An Optimal Control Problem of Backward Stochastic Differential Delay Equation
摘要:
本文研究了一个倒向随机微分时滞方程的最优控制问题。利用三个正倒向耦合的伴随方程，文中得到了最优控制满足的充分条件并给出一个最优消费选择的例子来说明理论结果的应用。
Abstract:
This paper studies an optimal problem of backward stochastic differential delay equation. By means of a three-coupled system of adjoint equations, we give a sufficient condition for optimal control. As an application, a financial example is presented to illustrate the theoretical result.
参考文献
|
[1]
|
Delong, L. and Imkeller, P. (2010) Backward Stochastic Differential Equations with Time Delayed Generators—Re- sults and Counter Examples. Annals of Applied Probability, 20, 1512-1536. [Google Scholar] [CrossRef]
|
|
[2]
|
Chen, L. and Huang, J. (2015) Stochastic Maximum Principle for Controlled Backward Delayed System via Advanced Stochastic Differential Equation. Journal of Optimization Theory and Applications, 167, 1112-1135. [Google Scholar] [CrossRef]
|
|
[3]
|
Shi, J. and Wang, G. (2015) A Non-Zero Sum Differential Game of BSDE with Time-Delayed Generator and Applications. IEEE Transactions on Automatic Control, 61, 1959-1964. [Google Scholar] [CrossRef]
|
|
[4]
|
Peng, S. and Wu, Z. (1999) Fully Coupled Forward Backward Stochastic Differential Equations and Applications to Optimal Control. SIAM Journal on Control and Optimization, 37, 825-843. [Google Scholar] [CrossRef]
|
|
[5]
|
Wang, G. and Yu, Z. (2012) A Partial Information Non-Zero Sum Differential Game of Backward Stochastic Differential Equations with Applications. Automatica, 48, 342-352. [Google Scholar] [CrossRef]
|
|
[6]
|
Lim, A. and Zhou, X. (2001) Linear-Quadratic Control of Backward Stochastic Differential Equations. SIAM Journal on Control and Optimization, 40, 450-474. [Google Scholar] [CrossRef]
|