NO-ARBITRAGE AND EQUIVALENT MARTINGALE MEASURES - AN ELEMENTARY PROOF OF THE HARRISON-PLISKA THEOREM

We give a new proof of a key result to the theorem that in the discrete-time stochastic model of a frictionless security market the absence of arbitrage possibilities is equivalent to the existence of a probability measure Q which is absolute continuous with respect to the basic probability measure P with the strictly positive and bounded density and such that all security prices are martingales with respect to Q. The proof is elementary in a sense that it does not involve a measurable selection theorem.