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.

We are interested in computation of locating arbitrage in-nancial markets with frictions. We consider a model with a nitenumber of nancial assets and a nitenumber of possible states of nature. We derive a negative result on computational complexity of arbitrage in the case when securities are traded in integer numbers of shares and with a maximum amount of shares that can be bought for a xed price (asin reality). When these conditions are relaxed, we show that polynomial time algorithms can be obtained by applying linear programming tech-niques. We also establish the equivalence for no-arbitrage condition & optimal consumption portfolio.

In this paper we consider a financial market model with frictions which include transaction costs, bid-ask spread and taxes. By using optimization, linear and nonlinear programming and convex programming techniques, several necessary and sufficient conditions are derived for the weak no-arbitrage. Some results on state prices are also provided. The results of this paper can provide at least some theoretical insight to the problem.

A new minimax model on optimal portfolio selection with uncertainty of both randomness and estimation in inputs is established and the corresponding optimal portfolio is derived analytically. Based on this result, a sufficient condition for the existence and uniqueness of a nonnegative equilibrium price system under which the total demand and supply of each asset are equal is provided and an explicit formula for such a price system is obtained. Furthermore, some properties of the equilibrium are discussed.

本文引入在险收益（Eamings-at-Risk，EaR）的风险概念，并考虑连续时间Markowitz均值一方差型证券投资组合选择问题，其中度量风险的方差被替代为终端财富的在险收益。在Black-Scholes设置下，我们给出了均值一在险收益意义下的最优常数再调整（best constant-rebalanced）证券组合投资策略以及有效边界的显式表达式。这一结果可方便地应用于动态投资决策与管理的实践中。我们还给出概念与结论的一些经济学解释。