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 $$(\Omega,\mathcal{F},\{\mathcal{F}_t\}_{t=0}^T,P)$$ such that at time $$t$$ the $$i^{th}$$ component can be thought of as a price for the $$i^{th}$$ asset.

Mathematically, a CPP $$Z = (Z_t)_{t=0}^T$$ in a market with d-assets is an adapted process in $$\mathbb{R}^d$$ if Z is a martingale with respect to the physical probability measure $$P$$, and if $$Z_t \in K_t^+ \backslash \{0\}$$ 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 $$Q$$.