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WEIGHTED COMONOTONIC RISK SHARING UNDER HETEROGENEOUS BELIEFS

Published online by Cambridge University Press:  12 March 2020

Haiyan Liu
Haiyan Liu*
Affiliation:
Department of Mathematics and Department of Statistics and Probability, Michigan State University, East Lansing, MI48824, USA, E-mail: hliu@math.msu.edu
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Abstract

We study a weighted comonotonic risk-sharing problem among multiple agents with distortion risk measures under heterogeneous beliefs. The explicit forms of optimal allocations are obtained, which are Pareto-optimal. A necessary and sufficient condition is given to ensure the uniqueness of the optimal allocation, and sufficient conditions are given to obtain an optimal allocation of the form of excess of loss or full insurance. The optimal allocation may satisfy individual rationality depending on the choice of the weight. When the distortion risk measure is value at risk or tail value at risk, an optimal allocation is generally of the excess-of-loss form. The numerical examples suggest that a risk is more likely to be shared among agents with heterogeneous beliefs, and the introduction of the weight enables us to prioritize some agents as part of a group sharing a risk.

Keywords

Distortion risk measureheterogeneous beliefsindividual rationalityvalue at risktail value at riskC60G22
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 50 , Issue 2 , May 2020 , pp. 647 - 673
Copyright
© Astin Bulletin 2020

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