Finance: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 [math]\displaystyle{ (\Omega,\mathcal{F},\{\mathcal{F}_t\}_{t=0}^T,P) }[/math] such that at time [math]\displaystyle{ t }[/math] the [math]\displaystyle{ i^{th} }[/math] component can be thought of as a price for the [math]\displaystyle{ i^{th} }[/math] asset. Mathematically, a CPP [math]\displaystyle{ Z = (Z_t)_{t=0}^T }[/math] in a market with d-assets is an adapted process in [math]\displaystyle{ \mathbb{R}^d }[/math] if Z is a martingale with respect to the physical probability measure [math]\displaystyle{ P }[/math], and if [math]\displaystyle{ Z_t \in K_t^+ \backslash \{0\} }[/math] at all times [math]\displaystyle{ t }[/math] such that [math]\displaystyle{ K_t }[/math] is the solvency cone for the market at time [math]\displaystyle{ t }[/math].[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 [math]\displaystyle{ Z }[/math] and the EMM [math]\displaystyle{ Q }[/math].[citation needed]
References
- ↑ Schachermayer, Walter (November 15, 2002). The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time.
- ↑ 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.
- ↑ 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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