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Multivariate claim processes with rough intensities: Properties and estimation

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  • Hainaut, Donatien

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," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 269-287.
    • Handle: RePEc:eee:insuma:v:107:y:2022:i:c:p:269-287
    DOI: 10.1016/j.insmatheco.2022.08.010
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    References listed on IDEAS

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    More about this item

    Keywords

    Fractional Brownian motion; Rough volatility; Cox process; Compound Poisson process; Cyber-risk;
    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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