We unify and establish equivalence between pathwise and quasi-sure approaches to robust modelling of financial markets in discrete time. In particular, we prove a Fundamental Theorem of Asset Pricing and a Superhedging Theorem which both encompass the formulations of [ BN15  ] and [ BFH+16  ]. Furthermore we explain how to extend an \mathcal{M on a set \Omega to a pathwise duality without changing the superhedging price.
We unify and establish equivalence between the pathwise and the quasi-sure approaches to robust modelling of financial markets in discrete time. In particular, we prove a Fundamental Theorem of Asset Pricing and a Superhedging Theorem , which encompass the formulations of [ Bouchard, B., Nutz, M. (2015). Arbitrage and duality in nondominated discrete-time models. The Annals of Applied Probability, 25(2), 823-859 ] and [ Burzoni, M., Frittelli, M., Hou, Z., Maggis, M., Obloj, J. (2019). Pointwise arbitrage pricing theory in discrete time. Mathematics of Operations Research ]. In bringing the two streams of literature together, we also examine and relate their many different notions of arbitrage. We also clarify the relation between robust and classical \mathbb{P on a set of paths \Omega may be extended to a pathwise superhedging on \Omega without changing the superhedging price.
R
pathwise and
the pathwise and the
R
which both
, which
R
BN15
Bouchard, B.,
A
Nutz, M. (2015). Arbitrage and duality in nondominated discrete-time models. The Annals of Applied Probability, 25(2), 823-859
R
BFH+16
Burzoni, M., Frittelli, M., Hou, Z., Maggis, M.,
A
Obloj, J. (2019). Pointwise arbitrage pricing theory in discrete time. Mathematics of Operations Research
R
Furthermore we explain how to extend an \mathcal{M
In bringing the two streams of literature together, we also examine and relate their many different notions of arbitrage. We also clarify the relation between robust and classical \mathbb{P
R
\Omega
of paths \Omega may be extended
R
duality
superhedging on \Omega