Seminar on Stochastic Optimal Control

We propose a general framework for studying op.mal issue of CAT bonds in the presence of uncertainty of the parameters. In par.cular, the intensity of arrival of natural disasters is inhomogeneous and may depend on unknown parameters. Given a prior on the distribu.on 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 op.mal policy through a quasivaria .onal parabolic equa.on, which can be solved numerically. We provide examples of applica.on in the context of hurricanes in Florida.