成比例交易费用下的投资消费最优策略

交易费用的存在使得最优投资消费问题变得非常复杂。存在交易费用时，持续进行股票交易 将导致交易费用无限增加，因此不能频繁交易。文章对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解析形式进行了研究，在只考虑两种 资产的情况下，利用价值函数的凹性和近似性，通过变量代换，将HJB方程从偏微分方程（P DE）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。

Optimal Strategy of Consumption and Investment with Transaction Costs Charged

The introduction of transaction costs makes complex the optimal strategy of consumption and investment.With transaction costs charged,stocks cannot be traded heavily.This article studies the optimal strategy of consumption and investment for a HARA investor who has to pay transaction costs proportionally and wants to maximize the expected utility of finite/or infinite horizon.With a focus on the two assets,the HJB can be reduced from a PDE to an ODE by using the concavity and the homothetic property of the value function,.The analytic forms of the value functions in the transaction zone and HJB equation which the value function requires in the NT zone are given.