Journal
IIE TRANSACTIONS
Volume 47, Issue 4, Pages 358-372Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/0740817X.2014.919045
Keywords
Random target; portfolio optimization; marginal utility function; expected utility maximization; utility function; robust optimization
Funding
- NSF [CMMI-1131386]
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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-maker's 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-maker's 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 target's 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.
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