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Multivariate claim processes with rough intensities: Properties and estimation

Author

Listed:
  • Hainaut, Donatien

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

Abstract

A Rough process shares most of features of fractional Brownian motion with a small Hurst index and its sample paths exhibit a high ruggedness compared to those of a Brownian motion. This article studies a multivariate claim process in which the instantaneous probability of claim occurrences has a rough dynamic. In this setting, the claim arrival intensities have an infinite quadratic variation and are not semi-martingales. Nevertheless, the joint moment generating function of claim processes and the integral of claim arrival intensities admits a representation in terms of solutions of fractional differential equations. A numerical procedure is next proposed to filter the most likely sample path of rough intensities from time-series of claims. To illustrate this work, we estimate one- and two-dimensional rough models to time-series of cyber-attacks targeting medical and other services in the US from 2014 to 2018.

Suggested Citation

  • Hainaut, Donatien, 2022. "Multivariate claim processes with rough intensities: Properties and estimation," LIDAM Reprints ISBA 2022035, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2022035
    DOI: https://doi.org/10.1016/j.insmatheco.2022.08.010
    Note: In: Insurance: Mathematics and Economics, 2022, vol. 107, p. 269-287
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    Keywords

    Fractional Brownian motion ; rough volatility ; Cox process;
    All these keywords.

    JEL classification:

    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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