A Maximum Principle for Partial Information Backward Stochastic Control Problems with Applications
A Maximum Principle for Partial Information Backward Stochastic Control Problems with Applications
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DOI：
10.1137/080738465
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发表时间：
2009-06
期刊：
影响因子：
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通讯作者：
Jianhui Huang;Guangchen Wang;J. Xiong
中科院分区：
文献类型：
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作者：
Jianhui Huang;Guangchen Wang;J. Xiong
研究了倒向随机系统的部分信息控制问题。本文的主要贡献有三：（1）首先，我们得到了部分信息控制问题的一个新的随机最大值原理。我们的方法依赖于直接计算的衍生物的成本功能。(ii)其次，我们首次引入了两类部分信息线性二次型后向控制问题，并利用最大值原理对它们进行了研究。利用前向和后向随机微分滤波方程，得到了完全的显式解。(iii)最后，我们研究了一类完全信息随机养老基金优化问题，它可以看作是一般部分信息随机养老基金优化问题的一个特例。应用上述最大值原理，我们得到了封闭形式的最优贡献策略，并给出了一些相关的经济评论。
This paper studies the partial information control problems of backward stochastic systems. There are three major contributions made in this paper: (i) First, we obtain a new stochastic maximum principle for partial information control problems. Our method relies on a direct calculation of the derivative of the cost functional. (ii) Second, we introduce two classes of partial information linear-quadratic backward control problems for the first time and then investigate them using the maximum principle. Complete and explicit solutions are obtained in terms of some forward and backward stochastic differential filtering equations. (iii) Last but not least, we study a class of full information stochastic pension fund optimization problems which can be viewed as a special case of our general partial information ones. Applying the aforementioned maximum principle, we derive the optimal contribution policy in closed-form and present some related economic remarks.