私募基金管理者的收益定价、风险选择与契约设计

考虑到市场非完备和私募基金管理者风险厌恶的实际情形,本文根据效用无差别原理,得到基金管理者收益的确定性等价价值满足的偏微分方程,并运用有限差分法进行数值分析.结果表明:非系统风险溢价的增大使得收益价值与自有资金率呈递增但呈边际递减规律;管理者的风险选择决定于非系统风险和风险厌恶态度,在契约有限期的情形下,风险中性型管理者会选择无限大的基金波动率,风险厌恶程度低(高)的管理者会选择尽可能大(小)的基金波动率;并从确定性等价的角度讨论了契约设计问题.     

Maximum Principle for a Stochastic Optimal Control Problem and Application to Portfolio/Consumption Choice

We consider mainly an optimal control problem motivated by a portfolio and consumption choice problem in a financial market where the utility of the investor is assumed to have a given homogeneous form. A Pontryagin local maximum principle is obtained by using classical variational methods. We apply the result to make optimal portfolio and consumption decisions for the problem under consideration. The optimal selection coincides with the one obtained in Refs. 1 and 2, where the Bellman dynamic programming principle was used.     

Connection between an Exactly Solvable Stochastic Optimal Control Problem and a Nonlinear Reaction-Diffusion Equation

We present an exactly soluble optimal stochastic control problem involving a diffusive two-states random evolution process and connect it to a nonlinear reaction-diffusion type of equation by using the technique of logarithmic transformations. The work generalizes the recently established connection between the non-linear Boltzmann-like equations introduced by Ruijgrok and Wu and the optimal control of a two-states random evolution process. In the sense of this generalization, the nonlinear reaction-diffusion equation is identified as the natural diffusive generalization of the Ruijgrok–Wu and Boltzmann model.     

“关灯”游戏的数学建模与求解

对互联网上的一个数学游戏的控制问题,进行了一般性推广,运用数学建模的方法给出了其基于有限域上的线性方程组的数学模型及求解.     

一类非平稳随机传递系统的最佳非线性滤波及优化算法

运用最佳非线性滤波方法及优化算法,讨论了一类不完全数据与具有连续时间的非平稳随机过程的最佳控制问题,得到了这两种状态下的两个最佳控制数学模型,给出了这类非平稳随机传递系统的最佳编码与最佳译码的建立方法,为解决这类非平稳随机过程的最佳控制提供了一种有效可靠的解决方法.