论文标题
Malliavin微积分及其应用于内部人员的强大最佳组合
Malliavin calculus and its application to robust optimal portfolio for an insider
论文作者
论文摘要
内部信息和模型不确定性是现实中投资组合选择理论的两个不可避免的问题。本文研究了在模型不确定性下拥有一般内部信息的投资者的强大最佳投资组合策略。在数学理论的方面，我们提高了正向积分的某些特性，并使用malliavin conculus来得出预期的itô级公式。然后，我们使用前向积分来通过模型不确定性来制定内部交易问题。我们给出了强大的最佳投资组合的一半表征，并相对于内部信息过滤获得了驱动噪声$ W $的半明星分解，这将问题转向了非期望的随机差异游戏问题。我们通过随机最大原理给出了总表征。在考虑内部人员为“小”和“大”的两种典型情况时，我们给出了相应的BSDE来表征强大的最佳投资组合策略，并在Donsker $δ$函数的情况下得出了投资组合的封闭形式，并在小型内部人士的情况下得出了值。我们介绍了模拟结果，并在不同情况下对最佳策略进行经济分析。
Insider information and model uncertainty are two unavoidable problems for the portfolio selection theory in reality. This paper studies the robust optimal portfolio strategy for an investor who owns general insider information under model uncertainty. On the aspect of the mathematical theory, we improve some properties of the forward integral and use Malliavin calculus to derive the anticipating Itô formula . Then we use forward integrals to formulate the insider-trading problem with model uncertainty. We give the half characterization of the robust optimal portfolio and obtain the semimartingale decomposition of the driving noise $W$ with respect to the insider information filtration, which turns the problem turns to the nonanticipative stochastic differential game problem. We give the total characterization by the stochastic maximum principle. When considering two typical situations where the insider is `small' and `large', we give the corresponding BSDEs to characterize the robust optimal portfolio strategy, and derive the closed form of the portfolio and the value function in the case of the small insider by the Donsker $δ$ functional. We present the simulation result and give the economic analysis of optimal strategies under different situations.
