A revisit of the Borch rule for the Principal-Agent Risk-Sharing problem
Résumé
In this paper we provide a new approach to tackle the Principal-Agent Risk-Sharing problem using optimal stochastic control technics. Our analysis relies on an optimal decomposition of the expected utility of the Principal in terms of the reservation utility of the Agent. In particular, this allows us to derive the Borch rule as a necessary optimality condition for this decomposition to hold, which sheds a new light on this economic concept. As a by-product, this approach provides a class of risk-sharing plans that satisfy the Borch rule; class to which the optimal plan belongs.
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