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 .
In this paper we provide an alternative framework to tackle the first-best Principal-Agent problem under CARA utilities. This framework leads to both a proof of existence and uniqueness of the solution to the Risk-Sharing problem under very general assumptions on the underlying contract space . Our analysis relies on an optimal decomposition of the expected utility of the Principal in terms of the reservation utility of the Agent and works both in a discrete time and continuous time setting . As a by-product this approach provides a novel way of characterizing the optimal contract in the CARA setting, which is as an alternative to the widely used Lagrangian method, and some analysis of the optimum .
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a new approach
an alternative framework
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first-best
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problem under CARA utilities. This framework leads to both a proof of existence and uniqueness of the solution to the
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using optimal stochastic control technics
under very general assumptions on the underlying contract space
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. 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
and works both in a discrete time and continuous time setting
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,
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class of risk-sharing plans that satisfy the Borch rule; class to which the optimal plan belongs
novel way of characterizing the optimal contract in the CARA setting, which is as an alternative to the widely used Lagrangian method, and some analysis of the optimum