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,{ℱt}t=0T,P) such that at time t the ith component can be thought of as a price for the ith asset. Mathematically, a CPP Z=(Zt)t=0T in a market with d-assets is an adapted process in ℝd if Z is a martingale with respect to the physical probability measure P, and if Zt∈Kt+∖{0} at all times t such that Kt is the solvency cone for the market at time t.[1][2]

The CPP plays the role of an equivalent martingale measure in markets with transaction costs.[3] In particular, there exists a 1-to-1 correspondence between the CPP Z and the EMM Q.[citation needed]

## References

1. ↑ Schachermayer, Walter (November 15, 2002). The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time.
2. ↑ Yuri M. Kabanov; Mher Safarian (2010). Markets with Transaction Costs: Mathematical Theory. Springer. p. 114. ISBN 978-3-540-68120-5. https://archive.org/details/marketswithtrans00kaba.
3. ↑ Jacka, Saul; Berkaoui, Abdelkarem; Warren, Jon (2008). "No arbitrage and closure results for trading cones with transaction costs". Finance and Stochastics 12 (4): 583–600. doi:10.1007/s00780-008-0075-7.

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