3.8 Article

Conditional mean risk sharing in the individual model with graphical dependencies

Journal

ANNALS OF ACTUARIAL SCIENCE
Volume 16, Issue 1, Pages 183-209

Publisher

CAMBRIDGE UNIV PRESS
DOI: 10.1017/S1748499521000166

Keywords

Graphical models; Ising model; Decomposable graphs; Size-biased transform

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Conditional mean risk sharing is effective for distributing total losses within an insurance pool. This paper develops analytical results for this allocation rule in individual risk models with dependence based on network structures. The Ising model is utilized for modeling occurrences and loss amounts in a decomposable graphical model specific to each participant.
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.

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