A MODEL‐FREE VERSION OF THE FUNDAMENTAL THEOREM OF ASSET PRICING AND THE SUPER‐REPLICATION THEOREM

By Beatrice Acciaio, Mathias Beiglbock, Friedrich Penkner, Walter Schachermayer. 2013

189 citations recorded by the source corpus.

We propose a Fundamental Theorem of Asset Pricing and a Super‐Replication Theorem in a model‐independent framework. We prove these theorems in the setting of finite, discrete time and a market consisting of a risky asset S as well as options written on this risky asset. As a technical condition, we assume the existence of a traded option with a superlinearly growing payoff‐function, e.g., a power option. This condition is not needed when sufficiently many vanilla options maturing at the horizon T are traded in the market.

Subfields: Economics and Econometrics, Finance

View Paper: https://www.semanticscholar.org/paper/06266cd5b3521ff362e04d176dc7e513e6509c95

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Citations in the corpus

Exponential utility maximization under model uncertainty for unbounded endowments (2016, background): “probabilistic model and the consideration of a whole family of models as a consequence. This is not a new concept and since the seminal papers [16] and [24] it has gained a lot of attention, see e.g. [1, 3, 4, 6, 8, 12, 18, 28, 29, 30] and [9] for an overview. To state our problem more precisely, gi”
UTILITY MAXIMIZATION UNDER MODEL UNCERTAINTY IN DISCRETE TIME (2013, background): “The robust superhedging problem has been studied in several settings; see [1, 4, 6, 11, 13, 17, 23, 26, 32, 33], among others.”
An Explicit Martingale Version of the One-Dimensional Brenier's Theorem with Full Marginals Constraint (2016, unknown): “For models in discrete-time, we refer to Acciaio, Beiglböck, Penkner & Schachermayer[1], Beiglböck & Nutz [8], Beiglböck, Henry-Labordère & Touzi [6], Bouchard & Nutz [11], Campi, Laachir & Martini [14], Fahim & Huang [28], De Marco & Henry-Labordère [24].”
Complete Duality for Martingale Optimal Transport on the Line (2015, background): “, [1, 8, 12, 13, 14, 19, 33] for models in discrete time and [6, 10, 15, 17, 18, 21, 22, 29, 31, 32, 35, 37] for continuous-time models.”
Arbitrage and duality in nondominated discrete-time models (2013, methodology): “The recent paper [1] is the closest to our study.”
Martingale optimal transport and robust hedging in continuous time (2012, background): “However, several recent papers [3,8] study this question in discrete time.”
ROBUST FUNDAMENTAL THEOREM FOR CONTINUOUS PROCESSES (2014, background): “]. We also refer to [12] for a discussion of diﬀerent notions of arbitrage in the context of traded options. For versions of the robust fundamental theorem for discrete-time frictionless markets, see [1, 7, 8, 43]; for discrete-time markets with transaction costs, see [2, 3, 6, 19]. The second main ”