Risk Tuning With Generalized Linear Regression

23 Pages Posted: 1 Aug 2007

See all articles by R. Tyrrell Rockafellar

R. Tyrrell Rockafellar

University of Washington - Department of Mathmatics

Stanislav P. Uryasev

University of Florida

Michael Zabarankin

Stevens Institute of Technology - Department of Mathematical Sciences

Date Written: March 31, 2007

Abstract

A framework is set up in which linear regression, as a way of approximating a random variable by other random variables, can be carried out in a variety of ways, which moreover can be tuned to the needs of a particular model in finance, or operations research more broadly. Although the idea of adapting the form of regression to the circumstances at hand has already found advocates in promoting quantile regression as an alternative to classical least-squares approaches, it is carried here much farther than that. Axiomatic concepts of error measure, deviation measure and risk measure are coordinated with certain "statistics" that likewise say something about a random variable. Problems of regression utilizing these concepts are analyzed and the character of their solutions is explored in a range of examples. Special attention is paid to parametric forms of regression which arise in connection with factor models. It is argued that when different aspects of risk enter an optimization problem, different forms of regression ought to be invoked for each of those aspects.

Keywords: linear regression, error measures, deviation measures, risk measures

JEL Classification: C00, C60, C70

Suggested Citation

Rockafellar, R. Tyrrell and Uryasev, Stanislav P. and Zabarankin, Michael, Risk Tuning With Generalized Linear Regression (March 31, 2007). Available at SSRN: https://ssrn.com/abstract=1003864 or http://dx.doi.org/10.2139/ssrn.1003864

R. Tyrrell Rockafellar (Contact Author)

University of Washington - Department of Mathmatics ( email )

Box 354350
Seattle, WA 98195-4350
United States

Stanislav P. Uryasev

University of Florida ( email )

303 Weil Hall
Gainesville, FL 32611-6595
United States
352-392-3091 (Phone)
352-392-3537 (Fax)

HOME PAGE: http://www.ise.ufl.edu/uryasev/

Michael Zabarankin

Stevens Institute of Technology - Department of Mathematical Sciences ( email )

Hoboken, NJ 07030
United States

HOME PAGE: http://personal.stevens.edu/~mzabaran/

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