Abstract

http://ssrn.com/abstract=1833735
 
 

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Envelope Theorems in Banach Lattices


Marzia De Donno


Bocconi University - Department of Decision Sciences; Universita di Pisa - Department of Mathematics

Anna Battauz


Bocconi University - Department of Finance

Fulvio Ortu


Bocconi University - Department of Finance

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.

Number of Pages in PDF File: 30

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Date posted: May 10, 2011  

Suggested Citation

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

Contact Information

Marzia De Donno (Contact Author)
Bocconi University - Department of Decision Sciences ( email )
Via Roentgen 1
Milan, 20136
Italy
Universita di Pisa - Department of Mathematics ( email )
Largo B. Pontecorvo 5
I-56127 Pisa
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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