Optimal risk sharing under distorted probabilities |
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Authors: | Michael Ludkovski Virginia R Young |
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Institution: | (1) Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106, USA;(2) Department of Mathematics, University of Michigan, 530 Church St., Ann Arbor, MI 48109, USA |
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Abstract: | We study optimal risk sharing among n agents endowed with distortion risk measures. Our model includes market frictions that can either represent linear transaction
costs or risk premia charged by a clearing house for the agents. Risk sharing under third-party constraints is also considered.
We obtain an explicit formula for Pareto optimal allocations. In particular, we find that a stop-loss or deductible risk sharing
is optimal in the case of two agents and several common distortion functions. This extends recent result of Jouini et al.
(Adv Math Econ 9:49–72, 2006) to the problem with unbounded risks and market frictions.
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Keywords: | Distortion risk measures Comonotonicity Risk sharing Pareto optimal allocations |
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