We develop envelope theorems for optimization problems in which the value function takes values in a general Banach lattice. We consider both the special case of a convex choice set and a concave objective function and the more general case case of an arbitrary choice set and a general objective function. We apply our results to discuss the existence of a well-defined notion of marginal utility of wealth in optimal discrete-time, finite-horizon consumption-portfolio problems with an unrestricted information structure and preferences allowed to display habit formation and state dependency.
Battauz, A., De Donno, M., Ortu, F., Envelope theorems in Banach lattices and asset pricing, <<MATHEMATICS AND FINANCIAL ECONOMICS>>, 2015; 9 (4): 303-323. [doi:10.1007/s11579-015-0145-5] [http://hdl.handle.net/10807/168924]
Envelope theorems in Banach lattices and asset pricing
De Donno, Marzia;
2015
Abstract
We develop envelope theorems for optimization problems in which the value function takes values in a general Banach lattice. We consider both the special case of a convex choice set and a concave objective function and the more general case case of an arbitrary choice set and a general objective function. We apply our results to discuss the existence of a well-defined notion of marginal utility of wealth in optimal discrete-time, finite-horizon consumption-portfolio problems with an unrestricted information structure and preferences allowed to display habit formation and state dependency.
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