Decision making under model uncertainty with applications in finance and insurance

The lack of a single stochastic model compatible with the available data initiates the need for developing robust decision making tools which account for the possibility of multiple stochastic models describing the phenomenon under consideration. Such questions have concerned the scientific community  at least since the 1950’s  (starting by the seminal contributions  of Alais and Elsberg) and have led to an important body of research,  linked with a number of Nobel prize awards, with highlight the introduction of the robust control formulation of decision making models under uncertainty, using the technique of penalizing models in terms of the Kuhlback-Leibler entropy, by Hansen and Sargent in the turn of the 21st century.

The aim of this talk is twofold:

1. To present some recent advances to the theory and applications of robust control for the study of problems in financial and actuarial risk management with concrete examples in portfolio management and pension fund management.
2. Present an alternative framework for quantifying model uncertainty, based on the theory of optimal transportation, by introducing of the concept of the Frechet risk measures or variational utilities and illustrating it in terms of applications in finance and insurance.