Consistent pricing process explained

(\Omega, l{F},\{ l{F} _{t\}} ^{T,P)} ^{t =0} 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} ^{t =0} 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} \backslash \{ 0 \} at all times t such that K _{t} 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 .

Notes and References

1. Schachermayer. Walter. November 15, 2002. The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time.
2. Book: Markets with Transaction Costs: Mathematical Theory. limited. Yuri M. Kabanov. Mher Safarian. Springer. 2010. 978-3-540-68120-5. 114.
3. No arbitrage and closure results for trading cones with transaction costs. Saul. Jacka. Abdelkarem. Berkaoui. Jon. Warren. Finance and Stochastics. 12. 4 . 583–600. 10.1007/s00780-008-0075-7. 2008. math/0602178. 17136711 .