Stochastic models have long been successfully applied to describe financial markets, make investment decisions, price and hedge financial derivatives, and manage risks. But this has led to an over-reliance on particular models and a disregard of the possibility of model misspecification. While in most engineering applications robust methods have a long history, the standard approach in mathematical finance is still to describe all underlying uncertainty with a single probability measure. However, in many real-life situations it is not possible to determine the precise probabilities of future events, and financial decision rules that are sensitive to particular assumptions can lead to disastrous outcomes if reality does not exactly unfold as predicted by the model. The goal of this project is to develop methods of financial decision-making that take into account extreme events and are robust with respect to model misspecification. The outcomes are expected to lead to robust approaches to investing, asset pricing, hedging, and risk management. Graduate students are included in the work of the project.
The project aims to create robust methods that can be used to address relevant problems in mathematical finance. Discrete-time as well as continuous-time models are studied. The plan is to establish non-linear Riesz representation results that can be used to develop robust versions of the fundamental theorem of asset pricing together with corresponding pricing duality formulas, robust methods for pricing and hedging options, as well as approaches to treat optimal asset allocation problems under model uncertainty. The problems to be addressed lie at the intersection of mathematical finance, investment theory, and financial economics. Methods from probability theory, stochastic analysis, functional analysis, and decision theory are used.
