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 $(\mathrm{\Omega },ℱ,\{{ℱ}_t{\}}_{t=0}^T,P)$ 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 ${ℝ}^d$ if Z is a martingale with respect to the physical probability measure $P$, and if $Z_t\in K_t^{+}\mathrm{\setminus }\{0\}$ 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 $Q$.Template:Citation needed

References

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