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# Accession Number:

## ADA616353

# Title:

## New Developments in Uncertainty: Linking Risk Management, Reliability, Statistics and Stochastic Optimization

# Descriptive Note:

## Final rept. Sep 2011-Nov 2014

# Corporate Author:

## FLORIDA UNIV GAINESVILLE DEPT OF INDUSTRIAL AND SYSTEMS ENGINEERING

# Report Date:

## 2014-11-13

# Pagination or Media Count:

##
43.0

# Abstract:

## Random variables that stand for cost, loss or damage must be confronted in numerous situations. Dealing with them systematically for purposes in risk management, optimization and statistics is the theme of this project, 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 which can substitute for the otherwise uncertain outcomes in a formulation of constraints and objectives. Such quantifications 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 familiar concept for dealing with gains instead of losses, but regret concerns hazards relative to a benchmark. It bridges risk measures and expected utility, thereby reconciling those two approaches to optimization under uncertainty. Statistical estimation is inevitably a partner with risk management in handling hazards, which may be known only partially through a data base. However, a much deeper connection has come to light with statistical theory itself, in particular regression. Very general measures of error can associate with any hazard variable a statistic along with a deviation which quantifies the variables 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 developed here puts all of this together in a unified scheme.

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

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