On computation of arbitrage for markets with friction

Abstract

We are interested in computation of locating arbitrage in nancial markets with frictions. We consider a model with a nite number of nancial assets and a nite number 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 (as in reality). When these conditions are relaxed, we show that polynomial time algorithms can be obtained by applying linear programming techniques. We also establish the equivalence for no-arbitrage condition & optimal consumption portfolio.