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

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  • Avanzi, Benjamin
  • Taylor, Greg
  • Wong, Bernard
  • Yang, Xinda

Abstract

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 Lévy 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.

Suggested Citation

  • Avanzi, Benjamin & Taylor, Greg & Wong, Bernard & Yang, Xinda, 2021. "On the modelling of multivariate counts with Cox processes and dependent shot noise intensities," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 9-24.
    • Handle: RePEc:eee:insuma:v:99:y:2021:i:c:p:9-24
    DOI: 10.1016/j.insmatheco.2021.01.002
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    References listed on IDEAS

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    Cited by:

    1. Teng, Ye & Zhang, Zhimin, 2023. "Finite-time expected present value of operating costs until ruin in a Cox risk model with periodic observation," Applied Mathematics and Computation, Elsevier, vol. 452(C).
    2. Yang Miao & Kristina P. Sendova, 2024. "Advantages of Accounting for Stochasticity in the Premium Process," Risks, MDPI, vol. 12(10), pages 1-25, October.
    3. Daniel J. Geiger & Akim Adekpedjou, 2022. "Analysis of IBNR Liabilities with Interevent Times Depending on Claim Counts," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 815-829, June.

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    More about this item

    Keywords

    Dependency modelling; Cox process; Shot noise; Insurance claims counts; Micro-level model; Markov chain Monte Carlo;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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