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Infinitely stochastic micro reserving

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  • Maciak, Matúš
  • Okhrin, Ostap
  • Pešta, Michal

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.

Suggested Citation

  • Maciak, Matúš & Okhrin, Ostap & Pešta, Michal, 2021. "Infinitely stochastic micro reserving," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 30-58.
    • Handle: RePEc:eee:insuma:v:100:y:2021:i:c:p:30-58
    DOI: 10.1016/j.insmatheco.2021.04.007
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    References listed on IDEAS

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    Cited by:

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    2. Rodi Lykou & George Tsaklidis, 2021. "Particle Filtering: A Priori Estimation of Observational Errors of a State-Space Model with Linear Observation Equation," Mathematics, MDPI, vol. 9(12), pages 1-16, June.

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    More about this item

    Keywords

    Stochastic prediction; Marked point process; Hawkes process; Time-varying model; Dynamic panel data; Consistency; Risk valuation; Micro claims reserving;
    All these keywords.

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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