TY - UNPB
T1 - Quantitative Fundamental Theorem of Asset Pricing
AU - Acciaio, Beatrice
AU - Backhoff, Julio
AU - Pammer, Gudmund
PY - 2022
Y1 - 2022
N2 - In this paper we provide a quantitative analysis to the concept of arbitrage, that allows to deal with model uncertainty without imposing the no-arbitrage condition. In markets that admit ``small arbitrage", we can still make sense of the problems of pricing and hedging. The pricing measures here will be such that asset price processes are close to being martingales, and the hedging strategies will need to cover some additional cost. We show a quantitative version of the Fundamental Theorem of Asset Pricing and of the Super-Replication Theorem. Finally, we study robustness of the amount of arbitrage and existence of respective pricing measures, showing stability of these concepts with respect to a strong adapted Wasserstein distance.
AB - In this paper we provide a quantitative analysis to the concept of arbitrage, that allows to deal with model uncertainty without imposing the no-arbitrage condition. In markets that admit ``small arbitrage", we can still make sense of the problems of pricing and hedging. The pricing measures here will be such that asset price processes are close to being martingales, and the hedging strategies will need to cover some additional cost. We show a quantitative version of the Fundamental Theorem of Asset Pricing and of the Super-Replication Theorem. Finally, we study robustness of the amount of arbitrage and existence of respective pricing measures, showing stability of these concepts with respect to a strong adapted Wasserstein distance.
UR - https://arxiv.org/abs/2209.15037
U2 - 10.48550/ARXIV.2209.15037
DO - 10.48550/ARXIV.2209.15037
M3 - Preprint
BT - Quantitative Fundamental Theorem of Asset Pricing
PB - arXiv
ER -