Risk Optimization

Human decisions (economic and otherwise) are often made in the presence of uncertainties, that is, in advance of receiving all the necessary information. As a consequence, the outcome of a decision (e.g., returns, costs, times, losses) is typically a random quantity determined by the missing information. This exposes decision makers to risk, that is to the possibility that the outcome of their decisions is excessively undesirable.

Including measures of risk in an optimization problem offers the possibility to directly "shape" the distribution of the random outcome of interest. In turn, one gains the chance of directly controlling or minimizing risk. 

This course deals with optimizing in the presence of risk. Particularly, the course touches upon some of the classical results regarding modeling and quantifying risk and transfers these results into tractable optimization problems. These results include topics taken from utility theory, stochastic dominance, risk-reward models, chance-constraints, Value-at-Risk, Conditional Value-at-Risk, coherent measures of risk, time-consistent measures of risk, deviation measures.

An exposition of the central theoretical results will be followed by practical project work on case studies inspired by real-life problems.