Envelope theorems in Banach lattices and asset pricing

Anna Battauz; Marzia De Donno; Fulvio Ortu

doi:10.1007/s11579-015-0145-5

Envelope theorems in Banach lattices and asset pricing

Anna Battauz, Marzia De Donno, Fulvio Ortu

Bocconi University

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	303-323
Number of pages	21
Journal	Mathematics and Financial Economics
Volume	9
DOIs	https://doi.org/10.1007/s11579-015-0145-5
Publication status	Published - 2015

Keywords

Banach lattice
Envelope theorem
Fréchet differential.
Gateaux differential
state-dependent utility
value function

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10.1007/s11579-015-0145-5

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title = "Envelope theorems in Banach lattices and asset pricing",

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.",

keywords = "Banach lattice, Envelope theorem, Fr{\'e}chet differential., Gateaux differential, state-dependent utility, value function, Banach lattice, Envelope theorem, Fr{\'e}chet differential., Gateaux differential, state-dependent utility, value function",

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year = "2015",

doi = "10.1007/s11579-015-0145-5",

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T1 - Envelope theorems in Banach lattices and asset pricing

AU - Battauz, Anna

AU - De Donno, Marzia

AU - Ortu, Fulvio

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

KW - Banach lattice

KW - Envelope theorem

KW - Fréchet differential.

KW - Gateaux differential

KW - state-dependent utility

KW - value function

KW - Banach lattice

KW - Envelope theorem

KW - Fréchet differential.

KW - Gateaux differential

KW - state-dependent utility

KW - value function

UR - http://hdl.handle.net/10807/168924

U2 - 10.1007/s11579-015-0145-5

DO - 10.1007/s11579-015-0145-5

M3 - Article

SN - 1862-9679

VL - 9

SP - 303

EP - 323

JO - Mathematics and Financial Economics

JF - Mathematics and Financial Economics

ER -

Envelope theorems in Banach lattices and asset pricing

Abstract

Keywords

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