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Conditional mean risk sharing in the individual model with graphical dependencies

Author

Listed:
  • Denuit, Michel

    (Université catholique de Louvain, LIDAM/ISBA, Belgium)

  • Robert, Christian Y.

Abstract

Conditional mean risk sharing appears to be effective to distribute total losses amongst participants within an insurance pool. This paper develops analytical results for this allocation rule in the individual risk model with dependence induced by the respective position within a graph. Precisely, losses are modelled by zero-augmented random variables whose joint occurrence distribution and individual claim amount distributions are based on network structures and can be characterised by graphical models. The Ising model is adopted for occurrences and loss amounts obey decomposable graphical models that are specific to each participant. Two graphical structures are thus used: the first one to describe the contagion amongst member units within the insurance pool and the second one to model the spread of losses inside each participating unit. The proposed individual risk model is typically useful for modelling operational risks, catastrophic risks or cybersecurity risks.

Suggested Citation

  • Denuit, Michel & Robert, Christian Y., 2022. "Conditional mean risk sharing in the individual model with graphical dependencies," LIDAM Reprints ISBA 2022020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2022020
    DOI: https://doi.org/10.1017/S1748499521000166
    Note: In: Annals of Actuarial Science, 2022, vol. 16(1), p. 183-209
    as

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    More about this item

    Keywords

    Graphical models ; Ising model ; decomposable graphs ; size-biased transform;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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