Centro de Documentacion de Fundación MAPFRE - A Minimum variance approach to multivariate linear regression with application to actuarial problems

MAP20260006307

A Minimum variance approach to multivariate linear regression with application to actuarial problems / Zinoviy Landsman and Udi Makov

Sumario: Variability is inherent in statistical, actuarial, and economic models, necessitating precise quantification for informed decision-making and risk management. Recently, Landsman and Shushi introduced the Location of Minimum Variance Squared Distance (LVS) risk functional, a novel variance-based measure of variability. We extend LVS to assess variability in regression models commonly used in actuarial analysis, enabling the construction of regression-type predictors in the Minimum Variance Squared Deviation (MVS) sense. We show that when the predicted vector Y follows a symmetric distribution, MVS aligns with the traditional Minimum Expected Squared Deviation (MES) functional. However, for non-symmetric distributions, MVS and MES diverge, with differences influenced by the joint third-moment matrix of distribution P and the covariance matrix of Y. We derive an analytical expression for MVS and explore a hybrid approach combining MVS and MES functionals. To illustrate the applicability of our approach, we present two numerical examples: (i) predicting three components of fire lossesbuildings, contents, and profitsand (ii) forecasting returns for six market indices based on the returns of their dominant stocks

En: European Actuarial Journal. - Cham, Switzerland : Springer Nature Switzerland AG, 2021-2022. - 15/12/2025 Volume 15 Issue 3 - December 2025 , 22 p.

1. Cálculo actuarial . 2. Análisis multivariante . 3. Predicciones estadísticas . 4. Gerencia de riesgos . 5. Análisis de varianza . 6. Big data . I. Makov, Udi E. . II. Título.