Refined Estimation of the Bellman Function for Stochastic Optimal Control Problems with Probabilistic Performance Criterion
In this paper, the optimal control problem for a discrete-time stochastic system with a general-form probabilistic criterion is considered. Using dynamic programming and the properties of the Bellman function, new two-sided bounds of this function that refine the earlier results are constructed. The...
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| Veröffentlicht in: | Automation and remote control 2019-04, Vol.80 (4), p.634-647 |
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| creator | Azanov, V. M. Kan, Yu. S. |
| description | In this paper, the optimal control problem for a discrete-time stochastic system with a general-form probabilistic criterion is considered. Using dynamic programming and the properties of the Bellman function, new two-sided bounds of this function that refine the earlier results are constructed. The derived bounds are then adopted to justify the application of the modified strategy that is optimal in the two-step investment portfolio management problem under risk to the corresponding multistep problem. An example that illustrates the advantages of such a strategy over other well-known strategies is given. |
| doi_str_mv | 10.1134/S0005117919040039 |
| format | Article |
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M.</creatorcontrib><creatorcontrib>Kan, Yu. S.</creatorcontrib><title>Refined Estimation of the Bellman Function for Stochastic Optimal Control Problems with Probabilistic Performance Criterion</title><title>Automation and remote control</title><addtitle>Autom Remote Control</addtitle><description>In this paper, the optimal control problem for a discrete-time stochastic system with a general-form probabilistic criterion is considered. Using dynamic programming and the properties of the Bellman function, new two-sided bounds of this function that refine the earlier results are constructed. The derived bounds are then adopted to justify the application of the modified strategy that is optimal in the two-step investment portfolio management problem under risk to the corresponding multistep problem. 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| ispartof | Automation and remote control, 2019-04, Vol.80 (4), p.634-647 |
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| source | Springer Nature - Complete Springer Journals |
| subjects | CAE) and Design Calculus of Variations and Optimal Control Optimization Computer-Aided Engineering (CAD Control Criteria Discrete time systems Dynamic programming Mathematics Mathematics and Statistics Mechanical Engineering Mechatronics Optimal control Portfolio management Robotics Stochastic Systems Systems Theory |
| title | Refined Estimation of the Bellman Function for Stochastic Optimal Control Problems with Probabilistic Performance Criterion |
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