Parameter Uncertainty and Residual Estimation Risk

Parameter Uncertainty and Residual Estimation Risk

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Article ID: iaor20163901
Volume: 83
Issue: 4
Start Page Number: 949
End Page Number: 978
Publication Date: Dec 2016
Journal: Journal of Risk and Insurance
Authors: ,
Keywords: risk, investment, forecasting: applications, statistics: distributions
Abstract:

The notion of residual estimation risk is introduced to quantify the impact of parameter uncertainty on capital adequacy, for a given risk measure and capital estimation procedure. Residual risk equals the risk measure applied to the difference between a random loss and the corresponding capital estimator. Modified estimation procedures are proposed, based on parametric bootstrapping and predictive distributions, which compensate the impact of parameter uncertainty and lead to higher capital requirements. In the particular case of location‐scale families, the analysis simplifies and a capital estimator can always be found that leads to a residual risk of exactly zero.

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