Optimal investment and consumption under partial information
Optimal investment and consumption under partial information
复制标题
部分信息下的最优投资和消费
DOI：
10.1007/s00186-015-0521-1
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发表时间：
2016
影响因子：
1.2
通讯作者：
Kristoffer Lindensjö
中科院分区：
文献类型：
--
作者：
Kristoffer Lindensjö
本文提出了非马尔可夫Itô过程市场中部分信息最优投资和消费问题的统一方法。agent不能观察到随机局部平均收益率和Wiener过程，但可以观察到路径依赖的波动率、路径依赖的利率和资产价格。主要假设是资产价格波动是资产价格轨迹的非预期函数。效用函数具有通用性，满足标准条件。首先，我们证明了相应的完全信息市场是完备的，并在此背景下用标准方法解决了问题。其次，我们利用过滤理论将原来的部分信息问题转化为相应的完全信息问题，并证明了市场是观测完全的，即任何适应可观测过滤的或有权利要求都是可复制的。利用全信息问题的解，我们可以很容易地推导出原部分信息问题的解。
We present a unified approach for partial information optimal investment and consumption problems in a non-Markovian Itô process market. The stochastic local mean rate of return and the Wiener process cannot be observed by the agent, whereas the path-dependent volatility, the path-dependent interest rate and the asset prices can be observed. The main assumption is that the asset price volatility is a nonanticipative functional of the asset price trajectory. The utility functions are general and satisfy standard conditions. First, we show that the corresponding full information market is complete and in this setting we solve the problem using standard methods. Second, we transform the original partial information problem into a corresponding full information problem using filtering theory, and show that it follows that the market is observationally complete in the sense that any contingent claim adapted to the observable filtration is replicable. Using the solutions of the full information problem we then easily derive solutions to the original partial information problem.