On an optimal consumption problem for p-integrable consumption plans

Balder, EJ Erik; Pistorius, Martijn

doi:10.1007/pl00004126

Cited by 7 publications

(2 citation statements)

References 10 publications

(65 reference statements)

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“…which shows thatf is a maximizer. ⊓ ⊔ Remark 3.5 Balder and Pistorius [4] provide an existence result for a multi-good consumption problem with a not necessarily concave utility function on R m + . They impose on the utility function a growth condition that also involves the pricing density.…”

Section: Proof Of Theorem 33mentioning

confidence: 99%

Utility maximization with a given pricing measure when the utility is not necessarily concave

Reichlin

2013

Math Finan Econ

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We study the problem of maximizing expected utility from terminal wealth for a not necessarily concave utility function U and for a budget set given by one fixed pricing measure. We prove the existence and several fundamental properties of a maximizer. We analyze the (not necessarily concave) value function (indirect utility) u(x, U). In particular, we show that the concave envelope of u(x, U) is the value function u(x, U c) of the utility maximization problem for the concave envelope U c of the utility function U. The two value functions are shown to coincide if the underlying probability space is atomless. This allows us to characterize the maximizers for several model classes explicitly

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Section: Proof Of Theorem 33mentioning

confidence: 99%

Utility maximization with a given pricing measure when the utility is not necessarily concave

Reichlin

2013

Math Finan Econ

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“…This also explains why we could prove part (ii) independently from part (i). See [10] for some additional comments on how to handle the situation where the measure space may have atoms. (Replace | · | by the norm of X, but equip X with the weak topology.)…”

Section: Epiloguementioning

confidence: 99%

Comment on an Existence Result for a Noncoercive Nonconvex Variational Problem

Balder¹

2001

SIAM J. Control Optim.

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An essential improvement is given of a recent existence result of Crasta [G. Crasta, SIAM J. Control Optim., 38 (1999), pp. 237-253] for a nonconvex, noncoercive variational problem whose integrand does not depend on the state variable. This is shown to follow by the methods based on Fatou's lemma in several dimensions of [E. ]. The associated Euler-Lagrange inclusions follow from well-known optimality conditions for such problems [V. M. Alekseev, V. M. Tichimirov, and S. V. Fomin, Optimal Control, Consultants Bureau, New York, 1987; V. I.

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Convexity and Closure in Optimal Allocations Determined by Decomposable Measures

Artstein

2019

Vietnam J. Math.

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On an optimal consumption problem for p-integrable consumption plans

Abstract: A generalization is presented of the existence results for an optimal consumption problem of Aumann and Perles [4] and Cox and Huang [10]. In addition, we present a very general optimality principle.

Cited by 7 publications

References 10 publications

Utility maximization with a given pricing measure when the utility is not necessarily concave

Utility maximization with a given pricing measure when the utility is not necessarily concave

Comment on an Existence Result for a Noncoercive Nonconvex Variational Problem

Convexity and Closure in Optimal Allocations Determined by Decomposable Measures

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