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.

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。

本文研究摩擦市场中的最优消费-投资组合选择问题。当金融资产和自然状态个数为有限个以及摩擦局限于成比例的交易费时，可用原始市场或适当转换了的市场的无套利性来刻画最优消费一投资组合策略的存在性或充要条件。

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.