On a risk model with tree-structured Poisson Markov random field frequency, with application to rainfall events Article Swipe

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Hélène Cossette , B. M. Cote , Alexandre Dubeau , Étienne Marceau ·

YOU? · · 2024 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2412.00607

In many insurance contexts, dependence between risks of a portfolio may arise from their frequencies. We investigate a dependent risk model in which we assume the vector of count variables to be a tree-structured Markov random field with Poisson marginals. The tree structure translates into a wide variety of dependence schemes. We study the global risk of the portfolio and the risk allocation to all its constituents. We provide asymptotic results for portfolios defined on infinitely growing trees. To illustrate its flexibility and computational scalability to higher dimensions, we calibrate the risk model on real-world extreme rainfall data and perform a risk analysis.

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Multivariate statistics Poisson distribution Tree (set theory) Mathematics Markov chain Econometrics Statistics Statistical physics Computer science Combinatorics Physics

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2412.00607
PDF: https://arxiv.org/pdf/2412.00607
OA Status: green
Related Works: 10
OpenAlex ID: https://openalex.org/W4405033379

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DOI: https://doi.org/10.48550/arxiv.2412.00607

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Title: On a risk model with tree-structured Poisson Markov random field frequency, with application to rainfall events

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Type: preprint

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Language: en

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Publication year: 2024

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Publication date: 2024-11-30

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Authors: Hélène Cossette, B. M. Cote, Alexandre Dubeau, Étienne Marceau

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Landing page: https://arxiv.org/abs/2412.00607

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PDF URL: https://arxiv.org/pdf/2412.00607

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Concepts: Multivariate statistics, Poisson distribution, Tree (set theory), Mathematics, Markov chain, Econometrics, Statistics, Statistical physics, Computer science, Combinatorics, Physics

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