Martingale Approach to Stochastic Control with Discretionary Stopping
Martingale Approach to Stochastic Control with Discretionary Stopping
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DOI：
10.1007/s00245-005-0841-2
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发表时间：
2006-02
影响因子：
1.8
通讯作者：
I. Karatzas;I. Zamfirescu
中科院分区：
文献类型：
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作者：
I. Karatzas;I. Zamfirescu
研究了具有任意停止的连续时间随机控制的鞅方法。给出了相应的动态规划方程和最大值原理。为控制策略的最优性提供了必要和充分条件;这些条件类似于Dubins和Savage（1976）在相关的离散时间背景下引入的“均衡”和“节俭”条件。建立了节俭控制策略的存在性。
We develop a martingale approach for continuous-time stochastic control with discretionary stopping. The relevant Dynamic Programming Equation and Maximum Principle are presented. Necessary and sufficient conditions are provided for the optimality of a control strategy; these are analogues of the "equalization" and "thriftiness" conditions introduced by Dubins and Savage (1976) in a related, discrete-time context. The existence of a thrifty control strategy is established.