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A multivariate aggregate loss model

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  • Ren, Jiandong

Abstract

In this paper, we introduce a multivariate aggregate loss model, where multiple categories of losses are considered. The model assumes that different types of claims arrive according to a Marked Markovian arrival process (MMAP) introduced by He and Neuts (1998) in the queuing literature. This approach enables us to allow dependencies among the claim frequencies, and among the claim sizes, as well as between claim frequencies and claim sizes. This model extends the (univariate) Markov modulated risk processes (sometimes referred to as regime switching models) widely used in insurance and financial analysis. For the proposed model, we provide formulas for calculating the joint moments of the present value of aggregate claims occurring in any time interval (0,t]. Numerical examples are provided to show possible applications of the model.

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  • Ren, Jiandong, 2012. "A multivariate aggregate loss model," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 402-408.
    • Handle: RePEc:eee:insuma:v:51:y:2012:i:2:p:402-408
    DOI: 10.1016/j.insmatheco.2012.06.009
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    References listed on IDEAS

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    Cited by:

    1. Ramírez-Cobo, Pepa & Carrizosa, Emilio & Lillo, Rosa E., 2021. "Analysis of an aggregate loss model in a Markov renewal regime," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    2. Övgücan Karadağ Erdemir, 2023. "A Comparative Perspective on Multivariate Modeling of Insurance Compensation Payments with Regression-Based and Copula-Based Models," EKOIST Journal of Econometrics and Statistics, Istanbul University, Faculty of Economics, vol. 0(39), pages 161-171, December.
    3. Hyunjoo Yoo & Bara Kim & Jeongsim Kim & Jiwook Jang, 2020. "Transform approach for discounted aggregate claims in a risk model with descendant claims," Annals of Operations Research, Springer, vol. 293(1), pages 175-192, October.
    4. Guillén, Montserrat & Sarabia, José María & Prieto, Faustino, 2013. "Simple risk measure calculations for sums of positive random variables," Insurance: Mathematics and Economics, Elsevier, vol. 53(1), pages 273-280.

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