General Arbitrage Pricing Model: II – Transaction Costs

In this paper we apply the general framework introduced in [2] to two models with transaction costs: • a dynamic model with an infinite number of assets; • a model with European call options as basic assets. In particular, it is proved that a dynamic model with an infinite number of assets satisfies the No Generalized Arbitrage condition (this notion was introduced in [2]) if and only if there exist an equivalent measure and a martingale with respect to this measure that lies (componentwise) between the discounted ask and bid price processes. Furthermore, the set of fair prices of a contingent claim coincides with the set of expectations of the payoff with respect to these measures. Our approach to arbitrage pricing in models with transaction costs differs from the existing ones. Key words: Delta-martingale, Fair price, Fundamental theorem of asset pricing, General arbitrage pricing model, Generalized arbitrage, Risk-neutral measure, Set of attainable incomes, Transaction costs