多资产下组成比例交易费用的投资消费最优策略

交易费用的存在使用最优投资消费策略问题非常复杂。当存在交易费用的时候,持续对股票进行交易将会导致交易费用无限增加。因此不能频繁进行股票交易。对只考虑两种资产的情况已经有较多的研究,但是对于多种资产的情况却没有引起人们的重视。本文对HARA效用函数下,有限期间和无限期间具有成比例交易费用的最优投资消费策略的价值函数的解析解进行了研究。在多种风险资产可以用来进行交易的情况下,利用价值函数的凹性和近似性,通过变量代换的方式,将HJB方程从偏微分方程(PDE)转化常微分方程(ODE),对价值函数进行求解,给出交易区解析解的形式和非交易区要满足的HJB方程。 

The Optimal Strategy of Consumption and Investment with Proportinal Transaction Costs and Multiple Risky Assets

The introduction of transaction costs adds considerable complexity to the optimal Consumption and Investment Strategy problem.In the presence of transaction costs,the stock is only traded infrequently.Policies for optimizing portfolios with multiple risky assets have received relatively less attention.This paper studies thve optimal Consumption and Investment Strategy for a HARA investor who faces proportional transaction costs and maximizes expected utility of finite/or infinite horizon.Multiple risky assets can be trading.Using the concavity and the homothetic property of the value function,the HJB can be reduced from a PDE to an ODE.The analytic forms of the value functions in the transaction regions are achieved and HJB equation which the value function must be satisfied with in the NT regions is given.