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Near-optimal control for stochastic recursive problems. (English) Zbl 1210.93083

Summary: It is well documented (e.g. X. Y. Zhou [SIAM J. Control Optimization 36, No. 3, 929–947 (1998; Zbl 0914.93073)]) that the near-optimal controls, as the alternative to the “exact” optimal controls, are of great importance for both the theoretical analysis and practical application purposes due to its nice structure and broad-range availability, feasibility as well as flexibility. However, the study of near-optimality on the stochastic recursive problems, to the best of our knowledge, is a totally unexplored area. Thus we aim to fill this gap in this paper. As the theoretical result, a necessary condition as well as a sufficient condition of near-optimality for stochastic recursive problems is derived by using Ekeland’s principle. Moreover, we work out an \(\varepsilon\)-optimal control example to shed light on the application of the theoretical result. Our work develops that of Zhou [loc. cit.] but in a rather different backward stochastic differential equation (BSDE) context.

MSC:

93E20 Optimal stochastic control
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
93C15 Control/observation systems governed by ordinary differential equations
49J52 Nonsmooth analysis
49K45 Optimality conditions for problems involving randomness

Citations:

Zbl 0914.93073
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Full Text: DOI

References:

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