obust models in mathematical finance replace the classical single probability measure by a sufficiently rich set of probability measures on the future states of the world to capture (Knightian) uncertainty about the “right” probabilities of future events. If this set of measures is nondominated, many results known from classical dominated frameworks cease to hold as probabilistic and analytic tools crucial for the handling of dominated models fail. We investigate the consequences for the robust model when prominent results from the mathematical finance literature are postulated. In this vein, we categorize the Kreps-Yan property, robust variants of the Brannath-Schachermayer bipolar theorem, Fatou representations of risk measures, and aggregation in robust models.

Model Uncertainty: A Reverse Approach / F. Liebrich, M. Maggis, G. Svindland. - In: SIAM JOURNAL ON FINANCIAL MATHEMATICS. - ISSN 1945-497X. - 13:3(2022 Oct), pp. 1230-1269. [10.1137/21M1425463]

Model Uncertainty: A Reverse Approach

M. Maggis;
2022

Abstract

obust models in mathematical finance replace the classical single probability measure by a sufficiently rich set of probability measures on the future states of the world to capture (Knightian) uncertainty about the “right” probabilities of future events. If this set of measures is nondominated, many results known from classical dominated frameworks cease to hold as probabilistic and analytic tools crucial for the handling of dominated models fail. We investigate the consequences for the robust model when prominent results from the mathematical finance literature are postulated. In this vein, we categorize the Kreps-Yan property, robust variants of the Brannath-Schachermayer bipolar theorem, Fatou representations of risk measures, and aggregation in robust models.
Robust mathematical finance; quasi-sure analysis; supported uncertainty; aggregation of random variables in robust models
Settore SECS-S/06 - Metodi mat. dell'economia e Scienze Attuariali e Finanziarie
Settore MAT/06 - Probabilita' e Statistica Matematica
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/943286
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