Managing Underperformance Risk in Project Portfolio Selection

We consider a project selection problem where each project has an uncertain return with partially characterized probability distribution. The decision maker selects a feasible subset of projects so that the risk of the portfolio return not meeting a specified target is minimized. To model and evaluate this risk, we propose and justify a general performance measure, the underperformance riskiness index (URI). We define a special case of the URI, the entropic underperformance riskiness index (EURI), for the project selection problem. We minimize the EURI of the project portfolio, which is the reciprocal of the absolute risk aversion (ARA) of an ambiguity-averse individual with constant ARA who is indifferent between the target return with certainty and the uncertain portfolio return. The EURI extends the riskiness index of Aumann and Serrano (2008) by incorporating the target and distributional ambiguity, and controls the underperformance probability (UP) for any target level. Our model includes correlation...

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