Mathematical models in finance
Mathematical models play a central role in several financial application, such as derivative pricing and credit risk. Multi-asset derivative pricing is an active field of research in financial modeling, calling for multivariate stochastic models. This research theme focus on the study of multivariate stochastic processes that reproduce well-known stylized facts such as skewness and excess kurtosis of marginal return distributions. In particular, we focus on multivariate Lèvy processes and multivariate additive processes. We also study multivariate distributions and their applications to credit risk modelling. In this framework, Bernoulli mixture models and multivariate Bernoulli distributions play a central role since they represent dependent default indicators.