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 .
We prove the Fundamental Theorem of Asset Pricing for a discrete time financial market where trading is subject to proportional transaction cost and the asset price dynamic is modeled by a family of probability measures, possibly non-dominated. Using a backward-forward scheme , we show that when the market consists of a money market account and a single stock, no-arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of consistent price systems. We also show that when the market consists of multiple dynamically traded assets and satisfiesefficient friction, strict no-arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of strictly consistent price systems .
R
consisting of a money market account and a single stock whose
where
R
whose
the asset
R
Under a continuity assumption, we prove using a
Using a
R
that the absence of arbitrage
, we show that when the market consists of a money market account and a single stock, no-arbitrage
R
A parallel statement between robust no-arbitrage and
We also show that when the market consists of multiple dynamically traded assets and satisfies
A
efficient friction
A
, strict no-arbitrage in a quasi-sure sense is equivalent to the existence of a suitable family of
D
is also obtained