One-Year Volatility of Reserve Risk in a Multivariate Framework

Yannick Appert-Raullin (yannick.appert@yahoo.fr), Laurent Devineau (ldevineau@gmail.com), Hinarii Pichevin (hinarii.pichevin@gmail.com) and Philippe Tann (tann.philippe@gmail.com)
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Yannick Appert-Raullin: Group Risk Management, GIE AXA - GIE AXA
Laurent Devineau: Recherche et Développement, Milliman Paris - Milliman France, LSAF - Laboratoire de Sciences Actuarielle et Financière - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon
Hinarii Pichevin: Recherche et Développement, Milliman Paris - Milliman France
Philippe Tann: Group Risk Management, GIE AXA - GIE AXA

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Abstract: The 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.

Keywords: 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 (search for similar items in EconPapers)
Date: 2013-07-30
New Economics Papers: this item is included in nep-for and nep-rmg
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