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Volume 37, Issue 3
Meshfree Approximation for Stochastic Optimal Control Problems

Sun Hui & Feng Bao

DOI: 10.4208/cmr.2021-0022

Commun. Math. Res., 37 (2021), pp. 387-420.

Published online: 2021-06

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  • Abstract

In this work, we study the gradient projection method for solving a class of stochastic control problems by using a mesh free approximation approach to implement spatial dimension approximation. Our main contribution is to extend the existing gradient projection method to moderate high-dimensional space. The moving least square method and the general radial basis function interpolation method are introduced as showcase methods to demonstrate our computational framework, and rigorous numerical analysis is provided to prove the convergence of our meshfree approximation approach. We also present several numerical experiments to validate the theoretical results of our approach and demonstrate the performance meshfree approximation in solving stochastic optimal control problems.

  • Keywords

Stochastic optimal control, maximum principle, backward stochastic differential equations, meshfree approximation.

  • AMS Subject Headings

93E20, 65K10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{CMR-37-387, author = {Hui , Sun and Bao , Feng}, title = {Meshfree Approximation for Stochastic Optimal Control Problems}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {37}, number = {3}, pages = {387--420}, abstract = {

In this work, we study the gradient projection method for solving a class of stochastic control problems by using a mesh free approximation approach to implement spatial dimension approximation. Our main contribution is to extend the existing gradient projection method to moderate high-dimensional space. The moving least square method and the general radial basis function interpolation method are introduced as showcase methods to demonstrate our computational framework, and rigorous numerical analysis is provided to prove the convergence of our meshfree approximation approach. We also present several numerical experiments to validate the theoretical results of our approach and demonstrate the performance meshfree approximation in solving stochastic optimal control problems.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2021-0022}, url = {http://global-sci.org/intro/article_detail/cmr/19266.html} }
TY - JOUR T1 - Meshfree Approximation for Stochastic Optimal Control Problems AU - Hui , Sun AU - Bao , Feng JO - Communications in Mathematical Research VL - 3 SP - 387 EP - 420 PY - 2021 DA - 2021/06 SN - 37 DO - http://doi.org/10.4208/cmr.2021-0022 UR - https://global-sci.org/intro/article_detail/cmr/19266.html KW - Stochastic optimal control, maximum principle, backward stochastic differential equations, meshfree approximation. AB -

In this work, we study the gradient projection method for solving a class of stochastic control problems by using a mesh free approximation approach to implement spatial dimension approximation. Our main contribution is to extend the existing gradient projection method to moderate high-dimensional space. The moving least square method and the general radial basis function interpolation method are introduced as showcase methods to demonstrate our computational framework, and rigorous numerical analysis is provided to prove the convergence of our meshfree approximation approach. We also present several numerical experiments to validate the theoretical results of our approach and demonstrate the performance meshfree approximation in solving stochastic optimal control problems.

Hui , Sun and Bao , Feng. (2021). Meshfree Approximation for Stochastic Optimal Control Problems. Communications in Mathematical Research . 37 (3). 387-420. doi:10.4208/cmr.2021-0022
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