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Conditional mean risk sharing in the individual model with graphical dependencies

Published online by Cambridge University Press:  17 June 2021

Michel Denuit  and
Christian Y. Robert Open the ORCID record for Christian Y. Robert [Opens in a new window]
Michel Denuit
Affiliation:
Institute of Statistics, Biostatistics and Actuarial Science – ISBA, Louvain Institute of Data Analysis and Modeling – LIDAM, UCLouvain, Louvain-la-Neuve1348, Belgium
Christian Y. Robert*
Affiliation:
Laboratory in Finance and Insurance – LFA, CREST – Center for Research in Economics and Statistics, ENSAE Paris, Palaiseau91120, France
*
*Corresponding author. E-mail: [email protected]
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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.

Keywords

Graphical modelsIsing modelDecomposable graphsSize-biased transformG22
Type
Original Research Paper
Information
Annals of Actuarial Science , Volume 16 , Issue 1 , March 2022 , pp. 183 - 209
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Institute and Faculty of Actuaries

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