Parametric and Nonparametric Bayesian Methods in Finance

The objective of the present thesis is to solve some relevant nancial problems through applications and generalizations of parametric and nonparametric Bayesian statistical methodologies. The increasing attention to Bayesian methodologies in all areas of science is due the clear-cut interpretation of the Bayesian approach, based on the posterior distribution of the parameters and on the posterior predictive of the observations, and to the more and more widely available powerful computational procedures. posterior can then be treated as the prior for the next period, and a new posterior is computed from new evidence. In the Bayesian non parametric approach (see Hjort et al. 2010 for a thorough state of the art), distributions can be unknown and treated as parameters. Thus, we need to construct potentially innite dimensional prior distributions on the space of all distribution functions. We focus on three areas: high-frequency nance, credit risk and state space models.