Consumption Portfolio Policies An Inverse Optimal Problem

Hua He

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4-', and A5, andC > for all W > and S > 0. Define R, H, N as in (31), (29), and (24), respectively, andQ, X, Y, and U as in (12), (13), (14), o. Nd (15) respectively. Suppose that (1) R, H, N satisfy the continuity and differentiability conditions of Conditions A3 and A6; and Here we remind the reader of our implicit hypothesis that the starting date of the optimization is t = but our arguments apply to other starting dates t with arbitrary starting states W(i) and S(t).
4 SUFFICIENT CONDITIONS... FOR EFFICIENCY AND RECOVER ABILITY 23 (2) conditions (l)-(6) of Theorem I are satisfied. Then (C, A) € S and the utility functions correspond to (C, A) are { U(C- l (x, S, t), S, t) x>0, M, J \ ]im ziQ U{C-\z, S, t), S, t) x = 0; hV(. ) = r "}r S sr\ X> °c Proof. See Appendix. I When C is not always strictly positive for strictly positive wealth, R cannot be defined through (31), and we have the second set of sufficient conditions. Note however that this set of conditions applies generally whenever VictS + T2K / 0, independently of whether C(W, S, t) > for all W > 0.

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