Time-inconsistent contract theory

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This paper investigates the moral hazard problem in finite horizon with both continuous and lump-sum payments, involving a time-inconsistent sophisticated agent and a standard utility maximiser principal.

• Building upon the so-called dynamic programming approach in Cvitani\'c, Possama\"i, and Touzi [18] and the recently available results in Hern\'andez and Possama\"i [43], we present a methodology that covers the previous contracting problem.
• Our main contribution consists in a characterisation of the moral hazard problem faced by the principal.
• In particular, it shows that under relatively mild technical conditions on the data of the problem, the supremum of the principal's expected utility over a smaller restricted family of contracts is equal to the supremum over all feasible contracts.