On computation of arbitrage for markets with friction

We. are interested in computation of locating arbitrage in financial markets with frictions. We consider a model with a finite number of financial assets and a finite 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 fixed price (as in reality). When these conditions axe 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.