Multivariate claim processes with rough intensities: Properties and estimation

Donatien Hainaut

Insurance: Mathematics and Economics, 2022, vol. 107, issue C, 269-287

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.

Keywords: Fractional Brownian motion; Rough volatility; Cox process; Compound Poisson process; Cyber-risk (search for similar items in EconPapers)
JEL-codes: C5 G22 (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:107:y:2022:i:c:p:269-287

DOI: 10.1016/j.insmatheco.2022.08.010

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