Infinitely stochastic micro reserving

Matúš Maciak, Ostap Okhrin and Michal Pešta

Insurance: Mathematics and Economics, 2021, vol. 100, issue C, 30-58

Abstract: Stochastic forecasting and risk valuation are now front burners in a list of applied and theoretical sciences. In this work, we 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 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 a simulation study. In the practical part of our exploration, we elaborate a specific actuarial application for micro claims reserving.

Keywords: Stochastic prediction; Marked point process; Hawkes process; Time-varying model; Dynamic panel data; Consistency; Risk valuation; Micro claims reserving (search for similar items in EconPapers)
JEL-codes: C13 C32 C33 C53 G22 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:100:y:2021:i:c:p:30-58

DOI: 10.1016/j.insmatheco.2021.04.007

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