具有流动性风险的终端财富效用最优化问题

发布时间：2018-01-12 08:19

本文关键词：具有流动性风险的终端财富效用最优化问题　出处：《上海交通大学》2012年硕士论文　论文类型：学位论文

【摘要】：本文考虑具有流动性风险的的无跳市场模型下，，投资策略的选择问题。本文的主要特点是，股票价格过程是一个连续时间的由布朗运动驱动的随机过程，由于市场的流动性，投资者只能在固定的时刻交易，在其余时间，投资者只能在旁观看。投资者的目标是，如何选择最优的投资策略，使得终端财富效用的期望达到最大。在本文中，我们引入一个典型的等弹性效用函数，考虑在此效用函数下的投资策略最优化问题，并且给出相应的最优终端财富过程及最优投资策略。 Huyên Pham and Peter Tankov(2009)[9]研究了具有流动性风险的市场模型中，如何实现消费效用最优化的问题，Michael Kohlmann and Dewen Xiong (2007)[18]在不具有流动性风险且带跳的金融市场模型中，研究了时-最优鞅测度的问题，并且在效用函数下给出实现最大效用的最优投资策略。类似Michael Kohlmann and Dewen Xiong (2007)[18]，我们首先引入一个新的测度，然后用动态规划的方法得到一个倒向鞅方程(BME)，然后证明了如果倒向鞅方程有解，当且仅当存在一个等价测度变换，使得终端财富过程能够被此测度变换的Radon-Nikodym导数来表示。最后，我们通过倒向鞅方程的解来表示出实现最大化期望的最优终端财富过程及最优投资策略。
[Abstract]:This paper has considered the liquidity risk of the market without jump model, choice of investment strategy. The main characteristics of this paper is that the stock price process is driven by the movement of Brown stochastic process is a continuous time, due to the liquidity of the market, investors can only trade at a fixed time, the rest of the time, investors can only in the the goal is to watch. Investors, how to choose the optimal investment strategy, which can maximize the expected utility from terminal wealth. In this paper, we introduce a classical utility function, consider the investment strategy optimization problem under this utility function, the optimal terminal wealth process and the optimal investment strategy and the corresponding.
The Huy n Pham and Peter Tankov (2009) [9] on the market model with liquidity risk, how to realize the consumer utility optimization problem, Michael Kohlmann and Dewen Xiong (2007) [18] in the financial market model with liquidity risk and jump, the optimal martingale measure. And the realization of the optimal investment strategy is given the maximum utility in the utility function. Similar to Michael Kohlmann and Dewen Xiong (2007) [18], we first introduce a new measure, and then use the dynamic programming method to obtain a backward martingale equation (BME), then it is proved that if the backward martingale equation is solved, and only when when there is an equivalent change of measure, so that the terminal wealth process can be the measure to transform Radon-Nikodym derivative. Finally, we through the backward martingale equation to represent the optimal terminal wealth maximization. The rich process and the best investment strategy.

【学位授予单位】：上海交通大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.91

【共引文献】