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A Variational Approach to the Maximization of Preferences Without Numerical Representation

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Abstract

We introduce a variational approach to study a maximization problem of preferences that cannot be represented by a utility function. In such conditions, we reformulate the problem as a suitable variational problem and we give regularity properties of the solutions map. The theoretical results are applied in studying an equilibrium problem under uncertainty.

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Notes

  1. Radner [33] presented an equilibrium model that generalizes the Debreu equilibrium to make the market institutions more realistic. The economy, evolving in T trade periods, is characterized by the possibility to trade, at each possible time and in each possible state that can occur, after the uncertainty is revealed and the market reopens and by the introduction of financial instruments that enable inter-temporal and insurance transfers of wealth through markets in each possible occurrence. The interested reader can refer to [29].

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Acknowledgements

We would like to thanks the referees for their insightful comments which led to an improved version of the present paper. Research of M. Milasi is partially supported by PRIN 2017 “Nonlinear Differential Problems via Variational, Topological and Set-valued Methods” (Grant Number: 2017AYM8XW).

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Authors and Affiliations

  1. Department of Economics, University of Messina, Messina, Italy

    Monica Milasi & Domenico Scopelliti

  2. Department of Economics and Managements, University of Pavia, Pavia, Italy

    Domenico Scopelliti

Authors
  1. Monica Milasi
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  2. Domenico Scopelliti
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Correspondence to Monica Milasi.

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Communicated by Juan Parra.

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Milasi, M., Scopelliti, D. A Variational Approach to the Maximization of Preferences Without Numerical Representation. J Optim Theory Appl 190, 879–893 (2021). https://doi.org/10.1007/s10957-021-01911-1

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