TY - JOUR
T1 - Risk tuning with generalized linear regression
AU - Rockafellar, R. Tyrrell
AU - Uryasev, Stan
AU - Zabarankin, Michael
PY - 2008/8
Y1 - 2008/8
N2 - 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.
AB - 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.
KW - Conditional value-at-risk
KW - Deviation measures
KW - Error measures
KW - Factor models
KW - Linear regression
KW - Portfolio optimization
KW - Quantile regression
KW - Risk management
KW - Risk measures
KW - Value-at-risk
UR - http://www.scopus.com/inward/record.url?scp=61349159348&partnerID=8YFLogxK
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U2 - 10.1287/moor.1080.0313
DO - 10.1287/moor.1080.0313
M3 - Article
AN - SCOPUS:61349159348
SN - 0364-765X
VL - 33
SP - 712
EP - 729
JO - Mathematics of Operations Research
JF - Mathematics of Operations Research
IS - 3
ER -