Measures of Residual Risk with Connections to Regression, Risk Tracking, Surrogate Models, and Ambiguity
Royset, Johannes O.
Rockafellar, R. Tyrrell
MetadataShow full item record
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.
RightsThis 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.
Showing items related by title, author, creator and subject.
Lawrance, A.J.; Lewis, P.A.W. (Wiley, 1985);An approach to modelling and residual analysis of nonlinear autoregressive time series in exponential variables is presented; the approach is illustrated by an analysis of a long series of wind velocity data which has first ...
Lewis, Peter A. W.; Lawrance, A. J. (Monterey, California. Naval Postgraduate School, 1984-08); NPS55-84-019An approach to modelling and residual analysis of nonlinear autoregressive time series in exponential variables is presented; the approach is illustrated by analysis of a long series of wind velocity data which has first ...
Rasmussen, Craig W.; Irvine, Cynthia E.; Dinolt, George W.; Levin, Timothy E. (DARPA DISCEX Conference, April 2003, 2003-04-00);Large complex systems need to be analyzed prior to operation so that those depending upon them for the protection of their information have a well defined understanding of the measures that have been taken to achieve ...