Regression Models in Risk Management

This chapter discusses theory and application of generalized linear regression that minimizes a general error measure of regression residual subject to various constraints on regression coefficients and includes least-squares linear regression, median regression, quantile regression, mixed quantile regression, and robust regression as special cases. Application of generalized linear regression includes examples of financial index tracking, sparse signal reconstruction, therapy treatment planning, collateralized debt obligation, mutual fund return-based style classification, and mortgage pipeline hedging. The chapter introduces risk envelopes and risk identifiers, and also states the error decomposition theorem. It discusses special types of unconstrained and constrained linear regressions encountered in statistical decision problems. Constrained least-squares linear regression is used in an intensity-modulated radiation therapy (IMRT) treatment-planning problem. Robust regression aims to reduce influence of sample outliers on regression parameters, especially when regression error has heavy tails.