Multivariate claim processes with rough intensities: properties and estimation
(2022) Insurance: Mathematics and Economics — Vol. 107, n° n/a/, p. 269-287 (2022)
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- 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.
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Citations
Hainaut, D. (2022). Multivariate claim processes with rough intensities: properties and estimation. Insurance: Mathematics and Economics, 107(n/a/), 269-287. https://doi.org/10.1016/j.insmatheco.2022.08.010 (Original work published 2022)