22 mai 2023

Nicolas Baradel (Ecole Polytechnique) and Roxana Dumitrescu (King's college, Londres)

Le 22 mai 2023

Nicolas Baradel : Optimal control under uncertainty: Application to the issue of CAT bonds

Résumé: We propose a general framework for studying optimal issue of CAT bonds in the presence of uncertainty on the parameters. In particular, the intensity of arrival of natural disasters is inhomogeneous and may depend on unknown parameters. Given a prior on the distribution of the unknown parameters, we explain how it should evolve according to the classical Bayes rule. Taking these progressive prior-adjustments into account, we characterize the optimal policy through a quasi-variational parabolic equation, which can be solved numerically. We provide examples of application in the context of hurricanes in Florida.

Roxana Dumitrescu : A new Mertens decomposition of Y g,ξ-submartingale systems and applications

Résumé: We  introduce the concept of Y g,ξ-submartingale systems, where the nonlinear operator Y g,ξ corresponds to the first component of the solution of a reflected BSDE with generator g and lower obstacle ξ. We first show that, in the case of a left-limited right-continuous obstacle, any Y g,ξ-submartingale system can be aggregated by a process which is right-lower semicontinuous. We then prove a Mertens decomposition, by using an original approach which does not make use of the standard penalization technique. These results are in particular useful for the treatment of control/stopping game problems and, to the best of our knowledge, they are completely new in the literature. We finally present two applications in Finance (based on joint works with R. Elie, W. Sabbagh and C. Zhou)