论文标题
强大效用最大化的二元性理论
Duality Theory for Robust Utility Maximisation
论文作者
论文摘要
在本文中，我们提出了一种二元性理论，用于连续时间在正真实轴上定义的效用函数的鲁棒效用最大化问题。我们的结果灵感来自Kramkov＆Schachermayer [18]的开创性工作的强大类似物。也就是说，我们表明，如果可实现的交易成果和定价措施集满足双极关系，那么效用最大化问题是与共轭问题双重性。我们进一步讨论了最佳交易策略的存在。特别是，我们的总体结果包括对数和功率实用程序的情况，它们适用于漂移和波动不确定性。
In this paper we present a duality theory for the robust utility maximisation problem in continuous time for utility functions defined on the positive real axis. Our results are inspired by -- and can be seen as the robust analogues of -- the seminal work of Kramkov & Schachermayer [18]. Namely, we show that if the set of attainable trading outcomes and the set of pricing measures satisfy a bipolar relation, then the utility maximisation problem is in duality with a conjugate problem. We further discuss the existence of optimal trading strategies. In particular, our general results include the case of logarithmic and power utility, and they apply to drift and volatility uncertainty.
