带交易费终端资产的期望效用最优化

Optimization Expected Utility of Terminal Wealth with Transaction Costs

研究了具有初始财富的投资者在一个带交易费的标准完全金融市场上如何最优化终端资产的期望效用.首先通过定义交易费用比例函数f(t),建立了连续时间投资模型,然后运用鞅分析和对偶理论得到了最优投资组合过程和终端财富,证明了在有效市场中,积极交易只会降低终端财富的期望值.

In this paper it is studied for an investor how to optimize expected utility of his terminal wealth in a standard complete market with transaction costs.Let f（t） be proportional function of transaction costs,we set up the investment model of continuous time.We get the optimal investment process and terminal wealth by using the convex dual function（Legendre transform） of the utility function and the theory of martingal.It is proved that active exchange does not improve the expected terminal wealth in the viable markets.