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Parameter uncertainty and residual estimation risk

Bignozzi, V. & Tsanakas, A. (2016). Parameter uncertainty and residual estimation risk. Journal of Risk and Insurance, 83(4), pp. 949-978. doi: 10.1111/jori.12075


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

Publication Type: Article
Additional Information: This is the peer reviewed version of the following article: Bignozzi, V. and Tsanakas, A. (2015), Parameter Uncertainty and Residual Estimation Risk. Journal of Risk and Insurance, which has been published in final form at This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.
Publisher Keywords: Parameter uncertainty; model uncertainty; bootstrap; predictive distribution; location-scale families; risk measures; solvency.
Subjects: H Social Sciences > HD Industries. Land use. Labor > HD61 Risk Management
H Social Sciences > HG Finance
Departments: Bayes Business School > Actuarial Science & Insurance
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