# 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 such that at time the component can be thought of as a price for the asset.

Mathematically, a CPP in a market with d-assets is an adapted process in if *Z* is a martingale with respect to the physical probability measure , and if at all times such that is the solvency cone for the market at time .[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 and the EMM .

## References

- Schachermayer, Walter (November 15, 2002). "The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time". Cite journal requires
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(help) - Yuri M. Kabanov; Mher Safarian (2010).
*Markets with Transaction Costs: Mathematical Theory*. Springer. p. 114. ISBN 978-3-540-68120-5. - 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. arXiv:math/0602178. doi:10.1007/s00780-008-0075-7.

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