Stochastic Finance, 4th Edition

1.5Geometric characterization of arbitrage-free models

The “fundamental theorem of asset pricing” in the form of Theorem 1.7 states that a market model is arbitrage-free if and only if the origin is contained in the set

where Y = (Y1, . . . , Yd) is the random vector of discounted net gains defined in (1.2). The aim of this section is to give a geometric description of the set M b(Y, P) as well as of the larger set

To this end, it will be convenient to work with the distribution

of Y with respect to P. That is, μ is a Borel probability measure ...