The Harrison-Pliska arbitrage pricing theorem under transaction costs

We consider a simple multi-asset discrete-time model of a currency market w ith transaction costs assuming the finite number of states of the nature. D efining two kinds of arbitrage opportunities we study necessary and suffici ent conditions for the absence of arbitrage. Our main result is a natural e xtension of the Harrison-Pliska theorem on asset pricing. We prove also a h edging theorem without supplementary hypotheses. (C) 2001 Elsevier Science B.V. All rights reserved.