Utility Maximization with Convex Constraints and Partial Information
Utility Maximization with Convex Constraints and Partial Information
复制标题
具有凸约束和部分信息的效用最大化
DOI：
10.1007/s10440-007-9124-z
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
Jörn Sass
中科院分区：
文献类型：
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作者：
Jörn Sass
考虑一个股票收益率满足随机微分方程的市场模型，该方程具有不可观测的随机漂移过程。投资者的目标是使最终财富的期望效用最大化，但投资决策仅基于对股票价格的了解。由此产生的高风险策略的性能可以大大提高通过施加凸约束，例如卖空限制。利用滤波方法，我们将模型转换为具有完整信息的模型。我们提供了一个验证结果，并显示如何在凸约束下的优化结果可以直接用于连续时间马尔可夫链模型的漂移。在特殊情况下，我们得到的最佳交易策略，包括随机波动率模型的表示。
We consider a market model where stock returns satisfy a stochastic differential equation with an unobservable, stochastic drift process. The investor’s objective is to maximize expected utility of terminal wealth, but investment decisions are based on the knowledge of the stock prices only. The performance of the resulting highly risky strategies can be improved considerably by imposing convex constraints covering e.g. short selling restrictions. Using filtering methods we transform the model to a model with full information. We provide a verification result and show how results on optimization under convex constraints can be used directly for a continuous time Markov chain model for the drift. In special cases we derive representations of the optimal trading strategies, including a stochastic volatility model.