典型效用指标下投资组合及消费选择的最优控制

Optimal Control in Investment Portfolio and Consumption under Typical Utility Index

研究两种股票的最优投资及消费问题.首先给出了金融市场中的随机模型,利用公式,得到了与消费及投资策略有关的财富过程的随机微分方程,并建立了最优消费与投资问题的随机控制模型.在随机干扰源相互关联的情形下,运用动态规划方法,对一类特殊的效用函数情形,得到了最优投资组合及消费选择的显性解.

The optimal investment portfolio and consumption policies of two stocks were studied.First of all,the stochastic model in the financial market was introduced.By using formula,the stochastic differential equation of wealth process concerning the decision of consumption and investment was given;the stochastic control model for consumption and investment was established.By using the dynamical programming method,the optimal investment portfolio and consumption policies for a particular kind of utility function were obtained under the condition of correlated random sources of disturbance.