Some Questions On The Fundamental Theorem Of Asset Pricing

A basic result in mathematical finance, sometimes called the fundamental theorem of asset pricing, is that for a stochastic process (St )t∈[0,T], the existence of an equivalentmartingale measure is "essentially" equivalent to the absence of arbitrage opportunities. In finance the process (St)t∈[0,T] describes the random evolution of the discounted price ofone or several financial assets. The equivalence of no-arbitrage with the existence of an equivalent probability martingale measure is at the basis of the entire theory of pricing by arbitrage . The relation between the concepts of arbitrage and equilibrium (which in turn is closely related to the notion of equivalent martingale measures in Mathematical Finance) has been an intensive object of research in the past two decades.Firstly, the survey to the fundamental theorem of assets pricing is carried on.a summary of generality to the existing achievements at present is done. Secondly another definition of arbitrage is provided and has been proved its equivalence with original arbitrage, and on this basis, the corresponding mathematics expression formula of arbitrage is given. Finally, to the particularity of the B- S model, any positive self-financing wealth process with initial value 1 is taken as the numeraire , then the conclusions in finance theory we cared about are received.