| 引用本文: | 徐可岱.带约束条件的最优停止问题.[J].国防科技大学学报,1985,(2):157-167.[点击复制] |
| Xu Kedai.On the Optimal Stopping Problem with Some Constrained Conditions[J].Journal of National University of Defense Technology,1985,(2):157-167[点击复制] |
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| 带约束条件的最优停止问题 |
| 徐可岱 |
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| 摘要: |
| 本文提出这样一类新的最优停止问题：设{xn,yn,ζn}∞n=1 是两个可积的适应随机序列，在使得Eyt≥Vy-a的停时类中求{xn,ζn}∞n=1的最优停时，其中a是一常数，Vy是{yn}∞n=1的值，且Vy＜∞。我们分别用Lagrange 方法和推广了的Snell外壳方法给出了存在性定理，并进行了一些比较，指出了对多目标最优停止问题的一个应用。 |
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| 投稿日期：1984-12-10 |
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| On the Optimal Stopping Problem with Some Constrained Conditions |
| Xu Kedai |
| Abstract: |
| In this paper we consider a new kind of optimal stopping problems. Let {xn,yn,ζn}∞n=1 be an integrable and adapted stochastic process. We will find an optimal stopping rule for {xn, ζn}∞n=1 in the class of stopping rule D such that for any t∈D，Eyt≥Vy-a， where α is a constant and Vy is the value of {yn, ζn}∞n=1 such that Vy＜∞.Adopting the Lagrange's method and the generalized Snell's method we obtain some existence theorems respectively，Finally，we discuss the two methods and apply them to solve the optimal stopping problem of the stochastic sequence of randon vectors. |
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