Multivariate rough claim processes: properties and estimation
(2022) , 27 pages
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- 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.
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Citations
Hainaut, D. (2022). Multivariate rough claim processes: properties and estimation (LIDAM Discussion Paper ISBA 2022/02). https://hdl.handle.net/2078.5/111876