Robust decision making over a set of random targets or risk-averse utilities with an application to portfolio optimization

Jian Hu, Sanjay Mehrotra*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

In many situations, decision-makers need to exceed a random target or make decisions using expected utilities. These two situations are equivalent when a decision-makers utility function is increasing and bounded. This article focuses on the problem where the random target has a concave cumulative distribution function (cdf) or a risk-averse decision-makers utility is concave (alternatively, the probability density function (pdf) of the random target or the decision-maker marginal utility is decreasing) and the concave cdf or utility can only be specified by an uncertainty set. Specifically, a robust (maximin) framework is studied to facilitate decision making in such situations. Functional bounds on the random targets cdf and pdf are used. Additional general auxiliary requirements may also be used to describe the uncertainty set. It is shown that a discretized version of the problem may be formulated as a linear program. A result showing the convergence of discretized models for uncertainty sets specified using continuous functions is also proved. A portfolio investment decision problem is used to illustrate the construction and usefulness of the proposed decision-making framework.

Original languageEnglish (US)
Pages (from-to)358-372
Number of pages15
JournalIIE Transactions (Institute of Industrial Engineers)
Volume47
Issue number4
DOIs
StatePublished - Apr 3 2015

Keywords

  • Expected utility maximization
  • Marginal utility function
  • Portfolio optimization
  • Random target
  • Robust optimization
  • Utility function

ASJC Scopus subject areas

  • Industrial and Manufacturing Engineering

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