Robust fundamental theorems of asset pricing in discrete time

Abstract

This paper is devoted to the study of robust fundamental theorems of asset pricing in discrete time and finite horizon settings. The new concept "robust pricing system" is introduced to rule out the existence of model independent arbitrage opportunities. Superhedging duality and strategy are obtained. * This work is supported by Center for Mathematical Modeling and Data Science, Osaka University. We thank Masaaki Fukasawa, Miklós Rásonyi and Martin Schweizer for constructive comments on the earlier version of the paper.

Super-replication with transaction costs under model uncertainty for continuous processes

“…The important point is that there are many other elements in C( θ, λ, A). This is explained in Subsection 3.5 of [12] where frictionless toy examples are presented.…”

“…In the present article we prove a fairly general superhedging theorem. We take a parametrization approach, different from the pathwise or quasi-sure settings, first used in [13], [40], see also [12]. As far as we know, the present paper is the first to apply to a wide range of continuous-time markets under transaction costs and model uncertainty.…”

“…First, we use the new topological framework of [12] for studying hedging under model uncertainty, this time in a continuous-time setting. The working space is the product topological vector space L ∞ = θ∈Θ (L ∞ , w * ) where we denote the product topology by w * .…”

“…This would necessitate finding a topological space in which the set of nice trading strategies is convexly compact. It would also be interesting to see if the present framework can be adapted to continuous-time frictionless markets, see [12] about what happens in the discrete-time case.…”

Super‐replication with transaction costs under model uncertainty for continuous processes

“…In the present article, we prove a fairly general superhedging theorem. We take a parametrization approach, different from the pathwise or quasi-sure settings, first used in Chau and Rásonyi (2019), Rásonyi and Meireles-Rodrigues (2021), see also Chau (2020). As far as we know, the present paper is the first to apply to a wide range of continuous-time markets under transaction costs and model uncertainty.…”