Abstract
Stochastic forecasting and risk valuation are now front burners in alist of applied and theoretical sciences. In this work, we propose anunconventional tool for stochastic prediction of future expenses based on the individual (micro) developments of recorded events.
Considering afirm, enterprise, institution, or any entity, which possesses knowledge about particular historical events, there might be awhole series of several related subevents: payments or losses spread over time. This all leads to an infinitely stochastic process at the end.
The aim, therefore, lies in predicting future subevent flows coming from already reported, occurred but not reported, and yet not occurred events. The emerging forecasting methodology involves marked time-varying Hawkes process with marks being other timevarying Hawkes processes.
The estimated parameters of the model are proved to be consistent and asymptotically normal under simple and easily verifiable assumptions. The empirical properties are investigated through asimulation study.
In the practical part of our exploration, we elaborate aspecific actuarial application for micro claims reserving. (C) 2021 Elsevier B.V. All rights reserved.