On the modelling of multivariate counts with Cox processes and dependent shot noise intensities

نویسندگان

چکیده

In this paper, we develop a method to model and estimate several, _dependent_ count processes, using granular data. Specifically, multivariate Cox process with shot noise intensities jointly the arrival of counts (e.g. insurance claims). The dependency structure is introduced via _intensity_ processes which are connected help L\'evy copulas. aggregate, our approach allows for (i) over-dispersion auto-correlation within each line business; (ii) realistic features involving time-varying, known covariates; (iii) parsimonious dependence between without requiring simultaneous primary accidents) events. explicit incorporation covariates can accommodate characteristics real data hence facilitate implementation in practice. an context, these could be changes policy volumes over time, as well seasonality patterns trends, may explain some relationship (dependence) multiple claims or at least tease out those relationships. Finally, filtering algorithm based on reversible-jump Markov Chain Monte Carlo (RJMCMC) latent stochastic illustrate calibration from AUSI set.

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ژورنال

عنوان ژورنال: Insurance Mathematics & Economics

سال: 2021

ISSN: ['0167-6687', '1873-5959']

DOI: https://doi.org/10.1016/j.insmatheco.2021.01.002