论文标题
随机漂移的多元金融市场中强大的效用最大化
Robust Utility Maximization in a Multivariate Financial Market with Stochastic Drift
论文作者
论文摘要
我们通过随机漂移过程研究金融市场中的实用性最大化问题，将最坏的方法与过滤技术相结合。资产价格很难估算漂移过程，同时，投资组合优化问题的最佳策略取决于漂移。我们通过设置一个最坏情况的优化问题来解决此问题，并为漂移的时间依赖性不确定性设置。投资者认为，不确定性集中的最糟糕的漂移过程将发生。这导致了本地优化问题，并且需要及时不断更新所得的最佳策略。我们证明了局部优化问题的最小定理并得出了最佳策略。此外，我们展示了如何根据过滤技术来定义椭圆形的不确定性集，并证明投资者需要选择强大的策略才能从其他信息中获利。
We study a utility maximization problem in a financial market with a stochastic drift process, combining a worst-case approach with filtering techniques. Drift processes are difficult to estimate from asset prices, and at the same time optimal strategies in portfolio optimization problems depend crucially on the drift. We approach this problem by setting up a worst-case optimization problem with a time-dependent uncertainty set for the drift. Investors assume that the worst possible drift process with values in the uncertainty set will occur. This leads to local optimization problems, and the resulting optimal strategy needs to be updated continuously in time. We prove a minimax theorem for the local optimization problems and derive the optimal strategy. Further, we show how an ellipsoidal uncertainty set can be defined based on filtering techniques and demonstrate that investors need to choose a robust strategy to be able to profit from additional information.
