In this paper, we focus on estimating ultimate claim counts in multiple insurance processes and thus extend the associated literature of micro-level stochastic reserving models to the multivariate context . Specifically, we develop a multivariate Cox process to model the joint arrival process of insurance claims in multiple Lines of Business . The dependency structure is introduced via multivariate shot noise intensity processes which are connected with the help of L\'evy copulas. Such a construction is more parsimonious and tractable in higher dimensions than plain vanilla common shock models. We also consider practical implementation and explicitly incorporate known covariates , such as seasonality patterns and trends, which may explain some of the relationship between two insurance processes( or at least help tease out those relationships ). We develop a filtering algorithm based on the reversible-jump Markov Chain Monte Carlo (RJMCMC) method to estimate the unobservable stochastic intensities . Model calibration is illustrated using real data from the AUSI data set.
In this paper, we develop a method to model and estimate several, _dependent_ count processes, using granular data . Specifically, we develop a multivariate Cox process with shot noise intensities to jointly model the arrival process of counts (e.g. insurance claims) . The dependency structure is introduced via multivariate shot noise _intensity_ processes which are connected with the help of L\'evy copulas. In aggregate, our approach allows for (i) over-dispersion and auto-correlation within each line of business; (ii) realistic features involving time-varying, known covariates; and (iii) parsimonious dependence between processes without requiring simultaneous primary (e.g. accidents) events. The explicit incorporation of time-varying, known covariates can accommodate characteristics of real data and hence facilitate implementation in practice. In an insurance context, these could be changes in policy volumes over time, as well as seasonality patterns and trends, which may explain some of the relationship (dependence) between multiple claims processes, or at least help tease out those relationships . Finally, we develop a filtering algorithm based on the reversible-jump Markov Chain Monte Carlo (RJMCMC) method to estimate the latent stochastic intensities and illustrate model calibration using real data from the AUSI data set.
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focus on estimating ultimate claim counts in multiple insurance processes and thus extend the associated literature of micro-level stochastic reserving models to the multivariate context
develop a method to model and estimate several, _dependent_ count processes, using granular data
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to model the joint
with shot noise intensities to jointly model the
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insurance claims in multiple Lines of Business
counts (e.g. insurance claims)
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intensity processes
_intensity_ processes
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Such a construction is more parsimonious and tractable in higher dimensions than plain vanilla common shock models. We also consider practical implementation and explicitly incorporate known covariates , such as
In aggregate, our approach allows for (i) over-dispersion and auto-correlation within each line of business; (ii) realistic features involving time-varying, known covariates; and (iii) parsimonious dependence between processes without requiring simultaneous primary (e.g. accidents) events. The explicit incorporation of time-varying, known covariates can accommodate characteristics of real data and hence facilitate implementation in practice. In an insurance context, these could be changes in policy volumes over time, as well as
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between two insurance processes(
(dependence) between multiple claims processes,
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). We
. Finally, we
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unobservable stochastic intensities . Model calibration is illustrated
latent stochastic intensities and illustrate model calibration