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Optimal Estimation Under Linear Constraints

Published online by Cambridge University Press:  29 August 2014

Walther Neuhaus
Walther Neuhaus*
Affiliation:
University of Copenhagen and UNI Storebrand ASA (Oslo)
*
Walther Neuhaus, UNI Storebrand ASA, P.O. Box 1380 Vika, N-0114 Oslo, Norway
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Abstract

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This paper shows how a multivariate Bayes estimator can be adjusted to satisfy a set of linear constraints. In the direct approach, the constraint is enforced by a restriction on the class of admissible estimators. In an alternative approach, the constraint is merely encouraged by a mixed risk function which penalises misbalance between the estimator and the constraint. The adjustment to the optimal unconstrained estimator is shown to depend on the risk function and the linear constraints only, not on the probability model underlying the Bayes estimator. Two practical examples are given, one of which involves reconciliation of independently assessed share values with current market values.

Keywords

Bayes EstimationLinear Bayes EstimationCredibility TheoryShare Valuation
Type
Workshops
Information
ASTIN Bulletin: The Journal of the IAA , Volume 26 , Issue 2 , November 1996 , pp. 233 - 245
Copyright
Copyright © International Actuarial Association 1996

References

Hogg, R.V. and Klugman, S.A. (1984) Loss Distributions. John Wiley & Sons.CrossRefGoogle Scholar
Gisler, A. (1987) Einige Bemerkungen zum hierarchischen Credibility-Modell. Mitteilungen der Vereinigung Schweizerischer Versicherungsmathematiker 1987, Heft 1: 91–98.Google Scholar
Neuhaus, W. (1995) Balanced Credibility Estimation. Applied Stochastic Models and Data Analysis 11, No. 3: 217–230.CrossRefGoogle Scholar
Sundt, B. (1992) On Greatest Accuracy Credibility with Limited Fluctuation. Scandinavian Actuarial Journal 1992, No. 2: 109–119.CrossRefGoogle Scholar
Taylor, G.C. (1992) A Bayesian Interpretation of Whittaker-Henderson Graduation. Insurance: Mathematics & Economics 11, No. 1: 7–16.Google Scholar