Multivariate rough claim processes: properties and estimation

Donatien Hainaut
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Donatien Hainaut: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2022002, LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: This article studies a multivariate claim process with stochastic intensities driven by rough mean reverting diffusions. By construction, the dynamic of claim arrivals is induced by a fractional Brownian motion with a Hurst index, H E(0,1/2). Therefore intensities have an infinite quadratic variation and are not semi-martingales. Nevertheless, we show that the moment generating function of the claim process admits a representation in terms of solutions of fractional differential equations. We next propose a procedure 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.

Keywords: Fractional Brownian motion; rough volatility; Cox process (search for similar items in EconPapers)
JEL-codes: C5 G22 (search for similar items in EconPapers)
Pages: 29
Date: 2022-01-22
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Persistent link: https://EconPapers.repec.org/RePEc:aiz:louvad:2022002

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