FTAP in finite discrete time with transaction costs by utility maximization

²Department of Mathematics, Technische Universitaet Muenchen Parkring 11, 85748 Garching, Germany
(email: martin.smaga@tum.de)

Abstract The aim of this paper is to prove the fundamental theorem of asset pricing (FTAP) in finite discrete time with proportional transaction costs by utility maximization. The idea goes back to L.C.G. Rogers' proof of the classical FTAP for a model without transaction costs. We consider one risky asset and show that under the robust no-arbitrage condition, the investor can maximize his expected utility. Using the optimal portfolio, a consistent price system is derived.

Key words: proportional transaction costs, arbitrage, consistent price system, fundamental theorem of asset pricing, utility