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

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The principal’s problem Theorem Let h p s denote (P)’s optimal wealth from time s onwards. Then: h p T = 0 h p t = ess sup U p t (h p t+1 −x−(β−1)A·∆˜P t+1)−c(A)∆t x∈F t+1 (A,β) +U a t (x+βA·∆˜P t+1) and u p 0 = W 0 − R + h p 0
The principal’s problem • (P) controls (A)’s wealth through x(= Ht+1 a − E ( ) t H a t+1 ) • x ∈ F t+1 (A, β) means that when faced <strong>with</strong> contract (β) and a future wealth prospect x, (A) chooses A • Problem can be reformulated in terms of (β, A) and Γ := X + βA · ∆˜P t+1 ∈ L 0 (F t+1 ) alone: ht p } = ess sup {U p t (h p t+1 +A·∆˜P t+1 −Γ)−c(A)∆t+Ut a(Γ) (A,β,Γ) (A,Γ)∈Ct (β)
Page 1 and 2: On portfolio delegation with moral
Page 3 and 4: Context • There is an investor (P
Page 5 and 6: The financial market, wealth and co
Page 7 and 8: Comments • The Agent’s optimiza
Page 9 and 10: Attainability Theorem (Existence of
Page 11: The Principal’s problem • If A
Page 15 and 16: Attainability of Principal’s prob
Page 17 and 18: Predictable representation property
Page 19 and 20: Markovian models Remark: Optimal ε
Page 21 and 22: Continuous-time analog • Define u
Page 23 and 24: To be better understood • Explore

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

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