The Fundamental Theorem of Asset Pricing Under Transaction Costs
35 Pages Posted: 23 Mar 2011 Last revised: 15 Apr 2012
Date Written: March 12, 2011
This paper proves the Fundamental Theorem of Asset Pricing with transaction costs, when bid and ask prices follow locally bounded cadlag (right-continuous, left-limited) processes. The Robust No Free Lunch with Vanishing Risk (RNFLVR) condition for simple strategies is equivalent to the existence of a strictly consistent price system (SCPS). This result relies on a new notion of admissibility, which reflects future liquidation opportunities. The (RNFLVR) condition implies that admissible strategies are predictable processes of finite variation.
The appendix develops an extension of the familiar Stieltjes integral for cadlag integrands and finite-variation integrators, which is central to modeling transaction costs with discontinuous prices.
Keywords: Arbitrage, Fundamental Theorem of Asset Pricing, Transaction Costs, Admissible Strategies, Finite Variation
JEL Classification: G12
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