本文用无套利方法分析有摩擦金融市场中利率的期限结构。对存在有限个债券和离散有限个到期日以及存在成比例的交易费、买卖差价、税赋这三种摩擦的金融市场。引入了相容期限结构的概念，给出了相容期限结构和套利机会的存在性结果或充要条件及它们的识别与计算方法。

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 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 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.

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.