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Decision Making under Uncertainty when Preference Information is Incomplete

Benjamin Armbruster (armbruster***at***northwestern.edu)
Erick Delage (erick.delage***at***hec.ca)

Abstract: We consider the problem of optimal decision making under uncertainty but assume that the decision maker's utility function is not completely known. Instead, we consider all the utilities that meet some criteria, such as preferring certain lotteries over certain other lotteries and being risk averse, s-shaped, or prudent. This extends the notion of stochastic dominance. We then give tractable formulations for such decision making problems. We formulate them as robust utility maximization problems, as optimization problems with stochastic dominance constraints, and as robust certainty equivalent maximization problems. We use a portfolio allocation problem to illustrate our results.

Keywords: decision making under uncertainty, expected utility, stochastic dominance, preference elicitation

Category 1: Stochastic Programming

Category 2: Robust Optimization

Category 3: Applications -- OR and Management Sciences (Finance and Economics )

Citation: Working draft

Download: [PDF]

Entry Submitted: 08/08/2011
Entry Accepted: 08/08/2011
Entry Last Modified: 06/29/2012

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