Necessary conditions in stochastic linear quadratic problems and their applications |
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Authors: | Tianxiao Wang |
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Affiliation: | School of Mathematics, Sichuan University, Chengdu, PR China |
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Abstract: | Stochastic linear quadratic optimal control problems are considered. A unified approach is proposed to treat the necessary optimality conditions of closed-loop optimal strategies and open-loop optimal controls. Notice that the former notion does not rely on initial wealth, while the later one does. Our conclusions of closed-loop optimal strategies are directly derived by suitable variational methods, the approach to which is different from [12], [11]. Moreover, the necessary conditions for closed-loop optimal strategies happen to be sufficient which takes us by surprise. Finally, two applications are given as illustration. |
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Keywords: | Stochastic linear quadratic problems Closed-loop optimal strategies Open-loop optimal controls Variational approach |
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