Envelope theorems in Banach lattices
AbstractWe derive envelope theorems for optimization problems in which the value function takes values in a general Banach lattice, and not necessarily in the real line. We impose no restriction whatsoever on the choice set. Our result extend therefore the ones of Milgrom and Segal (2002). We apply our results to discuss the existence of a well-defined notion of marginal utility of wealth in optimal consumption-portfolio problems in which the utility from consumption is additive but possibly state-dependent and, most importantly, the information structure is not required to be Markovian. In this general setting, the value function is itself a random variable and, if integrable, takes values in a Banach lattice so that our general results can be applied.
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Bibliographic InfoPaper provided by IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University in its series Working Papers with number 396.
Date of creation: 2011
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This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-06-04 (All new papers)
- NEP-DGE-2011-06-04 (Dynamic General Equilibrium)
- NEP-UPT-2011-06-04 (Utility Models & Prospect Theory)
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- Battauz, Anna & De Donno, Marzia & Ortu, Fulvio, 2011. "Intertemporal asset pricing and the marginal utility of wealth," Journal of Mathematical Economics, Elsevier, vol. 47(2), pages 227-244, March.
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