A0283
Title: A minimum variance approach to linear regression with application to actuarial and financial problems
Authors: Zinoviy Landsman - University of Haifa (Israel) [presenting]
Udi Makov - University of Haifa (Israel)
Abstract: Uncertainty is intrinsic to statistical, actuarial, and economic models, necessitating accurate quantification for informed decision-making and risk management. A recent study introduces the location of minimum variance squared distance (LVS) risk functional, offering a novel measure of uncertainty. LVS is extended to assess uncertainty in regression models commonly used in actuarial analysis. This functional allows the generation of predictors in the sense of minimum variance squared deviation (MVS). In this context, it is shown that when predicted vector Y follows a symmetric distribution, MVS resembles the traditional minimum expected squared deviation (MES) functional. However, for non-symmetric distributions, MES and MVS exhibit disparities influenced by the joint third moments matrix of distribution P and the covariance matrix of vector Y. The analytical expression is derived for MVS, and a mixed combination of MVS and MES functionals is explored. Two numerical illustrations are provided predicting three components of fire losses: buildings, contents and profits, and predicting returns for six market indices using the returns of their dominant stocks.
