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。

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.

In this paper we study the computational problem of arbitrage in a frictional market with a finite number of bonds and finite and discrete times to maturity. Types of frictions under consideration include fixed and proportional transaction costs, bid-ask spreads, taxes, and upper bounds on the number of units for transaction. We obtain some negative result on computational diculty in general for arbitrage under those frictions: It is NP-complete to identify whether there exists a cash-and-carry arbitrage transaction and it is NP-hard to find an optimal cash-and-carry arbitrage transaction.

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.