论文标题
G-Martingale的G- uTibilation最大化方法
The G-Martingale Approach for G-Utility Maximization
论文作者
论文摘要
在本文中，我们通过G-Martingale方法研究代表投资者的G-实用性最大化问题，该方法在Peng \ cite \ cite {pe19}提出的G-期望空间的框架中。金融市场只有一种债券和股票，其不确定性为特征，其特征是g-brownian动议。 \ cite {wxz}的常规思想失败了，因为g-brownian运动的二次变化过程也是一个随机过程。为了克服这一困难，应提出扩展的非线性期望。首先提出了足够的G-效率最大化条件。在对数持久性的情况下，可以通过构建和解决几个G-FBSDE来获得最佳策略的明确解决方案，然后验证满足足够条件的最佳策略。作为一种应用，通过相同的方法获得了随机兴趣模型的明确解决方案。最佳战略的所有经济含义都与我们的直觉一致。
In this paper, we study representative investor's G-utility maximization problem by G-martingale approach in the framework of G-expectation space proposed by Peng \cite{Pe19}. Financial market has only a bond and a stock with uncertainty characterized by G-Brownian motions. The routine idea of \cite{Wxz} fails because that the quadratic variation process of a G-Brownian motion is also a stochastic process. To overcome this difficulty, an extended nonlinear expectation should be pulled in. A sufficient condition of G-utility maximization is presented firstly. In the case of log-utility, an explicit solution of optimal strategy can be obtained by constructing and solving a couple of G-FBSDEs, then verifying the optimal strategy to meet the sufficient condition. As an application, an explicit solution of a stochastic interest model is obtained by the same approach. All economic meanings of optimal strategies are consistent with our intuitions.
