Publication:
Measures of Residual Risk with Connections to Regression, Risk Tracking, Surrogate Models, and Ambiguity

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Authors
Royset, Johannes O.
Rockafellar, R. Tyrrell
Subjects
risk measures
residual risk
generalized regression
surrogate estimation
optimization under stochastic ambiguity
Advisors
Date of Issue
2015-05-20
Date
May 20, 2015
Publisher
Language
Abstract
Measures of residual risk are developed as extension of measures of risk. They view a random variable of interest in concert with an auxiliary random vector that helps to manage, predict, and mitigate the risk in the original variable. Residual risk can be exempli ed as a quanti cation of the improved situation faced by a hedging investor compared to that of a single-asset investor, but the notion reaches further with deep connections emerging with forecasting and generalized regression. We establish the fundamental properties in this framework and show that measures of residual risk along with generalized regression can play central roles in the development of risk-tuned approximations of random variables, in tracking of statistics, and in estimation of the risk of conditional random variables. The paper ends with dual expressions for measures of residual risk, which lead to further insights and a new class of distributionally robust optimization models.
Type
Article
Description
Series/Report No
Department
Operations Research (OR)
Other Units
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
U. S. Air Force Office of Scientific Research grant FA9550-11-1-0206
U. S. Air Force Office of Scientific Research grant F1ATAO1194GOO1
U. S. Air Force Office of Scientific Research grant F4FGA04094G003
DARPA grant HR0011412251
Funder
U. S. Air Force Office of Scientific Research grant FA9550-11-1-0206
U. S. Air Force Office of Scientific Research grant F1ATAO1194GOO1
U. S. Air Force Office of Scientific Research grant F4FGA04094G003
DARPA grant HR0011412251
Format
34 p.
Citation
R.T. Rockafellar and J.O. Royset, 2015, "Measures of Residual Risk with Connections to Regression, Risk Tracking, Surrogate Models, and Ambiguity," SIAM J. Optimization, Vol. 25, No. 2, pp. 1179–1208.
Distribution Statement
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.
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