Coherent Approaches to Risk in Optimization Under Uncertainty

Decisions often need to be made before all the facts are in. A facility must be built to withstand storms, floods, or earthquakes of magnitudes that can only be guessed from historical records. A portfolio must be purchased in the face of only statistical knowledge, at best, about how markets will perform. In optimization, this implies that constraints may need to be envisioned in terms of safety margins instead of exact requirements. But what does that really mean in model formulation? What guidelines make sense, and what are the consequences for optimization structure and computation? The idea of a coherent measure of risk in terms of surrogates for potential loss, which has been developed in recent years for applications in financial engineering, holds promise for a far wider range of applications in which the traditional approaches to uncertainty have been subject to criticism. The general ideas and main facts are presented here with the goal of facilitating their transfer to practical work in those areas.