One-Year Volatility of Reserve Risk in a Multivariate Framework
AbstractThe one-year prediction error (one-year MSEP) proposed by Merz and Wüthrich has become a market-standard approach for the assessment of reserve volatilities for Solvency II purposes. However, this approach is declined in a univariate framework. Moreover, Braun proposed a closed-formed expression of the prediction error of several run-off portfolios at the ultimate horizon by taking into account their dependency. This article proposes an analytical expression of the one-year MSEP obtained by generalizing the modeling developed by Braun to the one-year horizon with an approach similar to Merz and Wüthrich. A full mathematical demonstration of the formula has been provided in this paper. A case study is presented to assess the dependency between commercial and motor liabilities businesses based on data coming from a major international insurer.
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Date of creation: 30 Jul 2013
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multivariate reserving; correlation; run-off portfolio; prediction error; estimation error; process error; one-year multivariate reserve risk; claims development result; Solvency II; aggregation; dependency; lines of business;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-08-05 (All new papers)
- NEP-FOR-2013-08-05 (Forecasting)
- NEP-RMG-2013-08-05 (Risk Management)
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- Hess, Klaus Th. & Schmidt, Klaus D. & Zocher, Mathias, 2006. "Multivariate loss prediction in the multivariate additive model," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 185-191, October.
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