2nd Western Conference in Mathematical Finance

Paolo Guasoni

The Fundamental Theorem of Asset Pricing under Transaction Costs

This talk discusses the Fundamental Theorem of Asset Pricing with transaction costs, when bid and ask prices are potentially discontinuous 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. We also develop an extension of the familiar Stieltjes integral for cadlag integrands and finite-variation integrators, which is central to modeling transaction costs with discontinuous prices.