Non-dominated models in mathematical finance: a reverse perspective

• Applicant: Professor Dr. Gregor Svindland
• Subject Area: Mathematics
• Term: since 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 471178162

In mathematical finance so-called robust models are often applied to account for Knightian uncertainty, that is uncertainty about the right probabilistic model. Whereas in classical probability theory one typically postulates that the likeliness of a future event is given by a single probability measure, in the robust case---for instance due to incomplete information--- this probability measure is replaced by a family P of probability measures which appear to be reasonable models. If this family P is not dominated by any reference probability measure, we call the model non-dominated. In non-dominated models many probabilisitic and analytical properties, which are crucial to develop the classical mathematical finance theory in dominated models, are in general lost. This poses quite some challenges when studying such models. Mostly, these are overcome by choosing concrete models which display some nice structure (product spaces, Wiener space, etc.) or by making sufficient ad hoc assumptions on the model which allow for certain results/applications. However, our interest lies in the reverse perspective, that is which properties of P are necessary (and sufficient) to produce certain theory for non-dominated models. Understanding the implied structures and dependencies will allow to further unify the existing theory for non-dominated models. Moreover, we aim at a better understanding of which type of model is suited for certain given applications.

• DFG Programme: Research Grants