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Envelope Theorems in Banach Lattices

30 Pages Posted: 10 May 2011  

Marzia De Donno

Universita Degli Studi Di Parma

Anna Battauz

Bocconi University - Department of Finance

Fulvio Ortu

Bocconi University - Department of Finance

Date Written: May 6, 2011

Abstract

We 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.

Suggested Citation

De Donno, Marzia and Battauz, Anna and Ortu, Fulvio, Envelope Theorems in Banach Lattices (May 6, 2011). Available at SSRN: https://ssrn.com/abstract=1833735 or http://dx.doi.org/10.2139/ssrn.1833735

Marzia De Donno (Contact Author)

Universita Degli Studi Di Parma

via Kennedy 6
Parma, 43125
Italy

Anna Battauz

Bocconi University - Department of Finance ( email )

Via Roentgen 1
Milano, MI 20136
Italy

Fulvio Ortu

Bocconi University - Department of Finance ( email )

Via Roentgen 1
Milano, MI 20136
Italy

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