PhD Oral Exam - Oscar Alberto Quijano Xacur, Mathematics
When studying for a doctoral degree (PhD), candidates submit a thesis that provides a critical review of the current state of knowledge of the thesis subject as well as the student’s own contributions to the subject. The distinguishing criterion of doctoral graduate research is a significant and original contribution to knowledge.
Once accepted, the candidate presents the thesis orally. This oral exam is open to the public.
Bayesian Inference is used to develop a credibility estimator and a method to compute insurance premium risk loadings. Algorithms to apply both methods to Generalized Linear Models (GLMs) are provided. We call our credibility estimator the entropic premium. It is a Bayesian point estimator that uses the relative entropy as the loss function. The risk measures Value-at-Risk (VaR) and Tail-Value-at-Risk (TVaR) are used to determine premium risk loadings. Our method considers the number of insureds and their durations as random variables. A distribution to model the duration of risks is introduced. We call it unifed, it has support on the interval (0, 1), it is an exponential dispersion family and it can be used as the response distribution of a GLM.