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<p>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 losses—buildings, contents, and profits—and (ii) forecasting returns for six market indices based on the returns of their dominant stocks.</p>

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A Minimum Variance Approach to Multivariate Linear Regression with application to actuarial problems

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月6日

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  • Zinoviy Landsman,
  • Udi Makov

摘要

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 losses—buildings, contents, and profits—and (ii) forecasting returns for six market indices based on the returns of their dominant stocks.