| 引用本文: | 罗建书.一类随机差分方程的解序列的最优停止规则.[J].国防科技大学学报,1992,14(1):86-91.[点击复制] |
| Luo Jianshu.On Optimal Stopping Rules for Solutions of a Class of Stochastic Difference Equations[J].Journal of National University of Defense Technology,1992,14(1):86-91[点击复制] |
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| 一类随机差分方程的解序列的最优停止规则 |
| 罗建书 |
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(系统工程与应用数学系)
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| 摘要: |
| 设报酬序列{xn,?n,n≥0}满足随机差分方程xn+1=xn+an+bnεn+1 （ε1，ε2，…为白噪声序列)。本文讨论了用有限情形{xn，0≤n≤N}的 Snell 包逼近无限情形 {xn，n≥0}的
Snell包的条件，得到了xn=E(xn︱?nε)(?nε=σ{ε0，ε1，…,εn},ε0=0)的 Snell 包γn的分解形式和最优停时存在的条件。最后讨论了最优停止规则的迭代计算法，并得出了迭代过程在有限步停止的充分条件。 |
| 关键词: 最优停止，随机差分方程，Rasche 方法 |
| DOI： |
| 投稿日期：1990-09-30 |
| 基金项目: |
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| On Optimal Stopping Rules for Solutions of a Class of Stochastic Difference Equations |
| Luo Jianshu |
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(Department of System Engineering and App1ied Mathematics)
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| Abstract: |
| Payoff sequence(xn,?n,n≥0)satisfy the stochastic difference equation xn+1=xn+an+bnεn+1，n=0,1,2,…, whereεi,i=l, 2，…，is a white noise sequence. In this paper，we discussed the condition for Snell's envelope of(xn, n≥0)to be approached by using Snell's envelope of finit sequence(xn，0≤n≤N). We have obtained the decomposable representations of Snell's envelope of xn=E(xn︱?nε)，n=0，1，2，…，where ?nε=σ（εi，i=0,1,2,…,n）,ε0=0. It is proposed that the necessary and sufficient condition for σn=inf (m≥n，rm=Xm) is optimal stopping. At last，we discussed the iterative algorithm for optimal stopping rules and obtained the sufficient condition under which the iterative process can be stopped in finit steps. |
| Keywords: optimal stopping,stochastic difference equation, Rasche method |
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