The Fundamental Risk Quadrangle in Risk Management, Optimization, and Statistical Estimation


Stan Uryasev
Director of Risk Management and Financial Engineering (RMFE) Lab
Industrial and Systems Engineering
University of Florida


Wednesday, October 30
4:15 - 5:15 PM


Abstract:

This presentation discusses the “Fundamental Quadrangle of Risk” framework including basic mathematical objects: Errors, Regrets, Risks, and Deviations. This framework suggests a consistent approach for defining and optimizing stochastic functions in various application areas. Random variables that stand for cost, loss or damage must be confronted in numerous situations. Dealing with them systematically in risk management, optimization and statistics is the theme of this presentation, which brings together ideas coming from many different areas. Measures of risk can be used to quantify the hazard in a random variable by a single value. Such quantification of risk can be portrayed on a higher level as generated from penalty-type expressions of "regret" about the mix of potential outcomes. A trade-off between an up-front level of hazard and the uncertain residual hazard underlies that derivation. Regret is the mirror image of utility, a concept for dealing with gains instead of losses. Measures of error can associate with any hazard variable a "statistic" along with a "deviation" which quantifies the variable's nonconstancy. Measures of deviation, on the other hand, are paired closely with measures of risk exhibiting "aversity." A direct correspondence can furthermore be identified between measures of error and measures of regret. The Fundamental Quadrangle of Risk puts all of this together in a unified scheme.

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Operations Research Colloquia: http://or.stanford.edu/oras_seminars.html