We study the optimal portfolio selection problem with transaction costs. In general, the ecient frontier can be determined by solving a parametric non-quadratic programming problem. In a general setting, the transaction cost is a V-shaped function of dierence between the existing and the new portfolio. We show how to transform this problem into a quadratic programming model. Hence a linear programming algorithm is applicable by establishing a linear approximation on the utility function of return and variance.

In this paper we study the optimal portfolio selection problem for assets. A doubleobjective programming model is Wrst formulated for selecting optimal portfolios of asserts with transaction costs and taxes, where short sales and borrowings are not allowed. Some properties of eYcient portfolios and the eYcient frontier to the model are then derived. Based on these results, an interactive method that requires only paired preference comparison from the investor is established for solving the optimal portfolio selection problem. A numerical example is also presented to illustrate this method.

本文根据均值-方差模型的框架，建立了用VaR代替方差或标准差作为风险的测量指标时的均值2VaR模型，同时使用等VaR线分析了两种模型的内在联系。作为模型的扩展本文还分别考虑了存在无风险资产，负债和非正态分布时的情形。此外讨论了均值2VaR模型有效边界的一些性质。

We are interested in computation of arbitrage condition in financial market with friction. We consider a deterministic model with a finite number of financial assets and a finite number of possible states of nature. The future return of of each asset under each possible state of nature is given in the model. We derive a negative result on computational complexity of arbitrage in the case when assets are traded in integer numbers of shares and with a maximum amount of shares that can be bought for a fixed price.

从经典的CRRA效用模型到近期关于LA和DA效用的研究，金融理论在新古典范式的基础上辅助了对行为和心理的分析。本文认为尤其值得指出的是，行为和心理研究带给金融学的新视角不仅从概念上对资产分配决策问题进行了革新，而且还逐渐将人们的行为特征模型化、数学化，这就大大推进了投资者在面临复杂的不确定性时的投资决策问题的研究。本文希望通过对CRRA、LA、DA三种效用模型的比较分析，对“不确定性”下的投资决策问题的研究提供有益的思路。