On portfolio delegation with moral hazard under translation ... - HIM

Attainability of Principal’s problem
Theorem
Suppose Ut a,p (·) = 1
γ
U a,p t (γ a,p·) and that U satisfies conditions for
attainability of Agent’s problem.
Then unconstrained problem has a solution, the optimal A ∗ attains
ess sup
{−c(A)∆t + 1 (
])
A
γ U γ
[h }
p t+1 + A∆˜P t+1
where γ = γa γ p
γ a +γ p , and Γ ∗ =
[
]
γp
γ a +γ
h p p t+1 + A∗ ∆˜P t+1 is optimal 5
5 Inspired by a similar result by Barrieu and El-Karoui