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The fundamental theorem of asset pricing under transaction costs. (English) Zbl 1262.91126

Summary: This paper proves the fundamental theorem of asset pricing with transaction costs, when bid and ask prices follow locally bounded càdlàg (right-continuous, left-limited) processes.
The “robust no-free-lunch with vanishing risk condition” (RNFLVR) 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 càdlàg integrands and finite-variation integrators, which is central to modelling transaction costs with discontinuous prices.

MSC:

91G10 Portfolio theory
91B25 Asset pricing models (MSC2010)
62P05 Applications of statistics to actuarial sciences and financial mathematics
26A45 Functions of bounded variation, generalizations
60H05 Stochastic integrals
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