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

The Agent’s problem
• (A)’s problem is a standard conditional optimization problem
• Let H a t
utility enjoyed by/promised to (A) from t ∈ T on:
H a T = ε T
H a t = ess sup
A∈L 0 (Ft ) N {U a t (H a t+1 +βtA·∆˜P t+1)−c t(A)∆t}
• Formally if H a t+1 = E ( H a t+1 |F t)
+ x
a
t+1 , we get a BS∆E:
∆Ht+1 a =xa t+1 − ess sup {U a
A∈L 0 (Ft ) N t (xt+1 a +βtA·∆˜P t+1)−c t(A)∆t}
• Controlling ε T steers H a (hence x a ) and makes H a 0 = R.
Therefore, reinterpret BS∆E as an S∆E starting from R