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Utilities bounded below

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  • Roman Muraviev
  • L. Rogers

Abstract

It is common to work with utilities which are not bounded below, but it seems hard to reconcile this with common sense; is the plight of a man who receives only one crumb of bread a day to eat really very much worse than the plight of a man who receives two? In this paper we study utilities which are bounded below, which necessitates novel modelling elements to prevent the question becoming trivial. What we propose is that an agent is subjected to random reviews of his finances. If he is reviewed and found to be bankrupt, then he is thrown into jail, and receives some large but finite negative value. In such a framework, we find optimal investment and consumption behaviour very different from the standard story. As the agent’s wealth goes negative, he gradually abandons hope of ever becoming honest again, and plunders as much as he can before being caught. Agents with very high wealth act like standard Merton investors. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Roman Muraviev & L. Rogers, 2013. "Utilities bounded below," Annals of Finance, Springer, vol. 9(2), pages 271-289, May.
    • Handle: RePEc:kap:annfin:v:9:y:2013:i:2:p:271-289
    DOI: 10.1007/s10436-012-0212-3
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    References listed on IDEAS

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    Cited by:

    1. Miklos Rasonyi, 2014. "Optimal investment with bounded above utilities in discrete time markets," Papers 1409.2023, arXiv.org.
    2. Mikl'os R'asonyi & Andrea Meireles Rodrigues, 2013. "Continuous-Time Portfolio Optimisation for a Behavioural Investor with Bounded Utility on Gains," Papers 1309.0362, arXiv.org, revised Mar 2014.

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    More about this item

    Keywords

    Expected utility; Non-concave utility; Von Neumann-Morgenstern preferences; D01; D03;
    All these keywords.

    JEL classification:

    • D01 - Microeconomics - - General - - - Microeconomic Behavior: Underlying Principles
    • D03 - Microeconomics - - General - - - Behavioral Microeconomics: Underlying Principles

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