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.
Envelope theorems in Banach lattices and asset pricing / Battauz, Anna; DE DONNO, Marzia; Ortu, Fulvio. - In: MATHEMATICS AND FINANCIAL ECONOMICS. - ISSN 1862-9679. - (2015). [10.1007/s11579-015-0145-5]
Envelope theorems in Banach lattices and asset pricing
DE DONNO, Marzia;
2015-01-01
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.| File | Dimensione | Formato | |
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