Simultaneous risk events modeling by the Batch Markov-modulated poisson process

Abstract

The Batch Markovian Arrival Process (BMAP) is a general class of point processes suitable for the modeling of dependent and correlated batch events (as arrivals, failures or risk events). BMAPs have been widely considered in the literature from a theoretical viewpoint. However, less works are devoted to study statistical inference which is of crucial importance in operational risk contexts, often characterized by dependent and simultaneous failures. In this work, we consider the estimation for a wide subclass of BMAPs, namely, the Batch Markov-Modulated Poisson processes (BMMPP) which generalize the well-known Markov-Modulated Poisson process. A matching moments technique, supported by a theoretical result that characterizes the process in terms of its moments, is considered. Numerical results with both simulated and real datasets related to operational risk will be presented to illustrate the performance of the novel approach.