Consistent pricing process

A consistent pricing process (CPP) is any representation of (frictionless) "prices" of assets in a market. It is a stochastic process in a filtered probability space ( Ω , F , { F t } t = 0 T , P ) such that at time t the i t h component can be thought of as a price for the i t h asset.

Mathematically, a CPP Z = ( Z t ) t = 0 T in a market with d-assets is an adapted process in R d if Z is a martingale with respect to the physical probability measure P , and if Z t ∈ K t + ∖ { 0 } at all times t such that K t is the solvency cone for the market at time t .

The CPP plays the role of an equivalent martingale measure in markets with transaction costs. In particular, there exists a 1-to-1 correspondence between the CPP Z and the EMM Q .