Fundamental Theorem of Asset Pricing under Transaction costs and Model uncertainty
Seminar Room 2, Newton Institute Gatehouse
We prove the Fundamental Theorem of Asset Pricing for a discrete time financial market consisting of a money market account and a single stock whose trading is subject to proportional transaction cost and whose price dynamic is modeled by a family of probability measures, possibly non-dominated. Under a continuity assumption, we prove using a backward-forward scheme that the absence of arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of consistent price systems. A parallel statement between robust no-arbitrage and strictly consistent price systems is also obtained.