Computation of arbitrage in a financial market with various types of frictions

Abstract

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 difficulty 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. © Springer-Verlag Berlin Heidelberg 2005.