Consistent pricing process

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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 (\Omega,\mathcal{F},\{\mathcal{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 \mathbb{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.[citation needed]

References[edit]

  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. 
  3. ^ Jacka, Saul; Berkaoui, Abdelkarem; Warren, Jon. "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.