Conditional mean risk sharing for dependent risks using graphical models

Conditional mean risk sharing appears to be e_ective in collaborative insurance to distribute total losses among participants. This paper develops analytical results for this risk sharing rule when risks are zero-augmented random variables whose joint occurrences distributions and claim amount distributions are based on network structures and may be characterized by graphical models. More speci_cally we consider the Ising model for occurrences and decomposable graphical models for the claim amount structures. Such models are typically useful for modeling operational risk or cyber security risk.