Přednášející: M. Pešta (MFF UK) Online přednáška. Přístup obdrží členové ČSpA a zapsaní studenti semináře.
Stochastic forecasting and risk valuation are now front burners in a list of applied and theoretical sciences. In our work we firstly propose an unconventional tool for stochastic prediction of future expenses based on the individual (micro) developments of recorded events. Considering a firm, enterprise, institution, or any entity, which possesses knowledge about particular historical events, there might be a whole 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 time-varying Hawkes processes. The maximum likelihood approach is employed. The estimated parameters are proved to be consistent and asymptotically normal undersimple and easily verifiable assumptions. The empirical properties are investigated through a simulation study. In the practical part of our exploration, we elaborate a specific actuarial application for micro claims reserving.