General Arbitrage Pricing Model: III – Possibility Approach

We introduce the possibility approach to pricing by arbitrage. The characteristic feature of this approach is that it does not employ the historic probability measure. The study is performed on two levels of generality: • for a static model with a finite number of assets; • for a general arbitrage pricing model introduced in [3]. The main results obtained for each of these models are: the fundamental theorem of asset pricing and the representation of the fair price intervals. Key words: Fair price, Fundamental theorem of asset pricing, General arbitrage pricing model, Generalized arbitrage, Possibility space, Risk-neutral measure, Set of attainable incomes, Set of possible elementary events, Transaction costs