One-Year Volatility of Reserve Risk in a Multivariate Framework

Yannick Appert-Raullin (1) , Laurent Devineau (2, 3) , Hinarii Pichevin (2) , Philippe Tann (1)

1 Group Risk Management, GIE AXA
2 Recherche et Développement, Milliman Paris
3 SAF - Laboratoire de Sciences Actuarielle et Financière

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.

Mots clés: 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

Domaines: Gestion des risques [q-fin.RM]

Yannick Appert-Raullin, Laurent Devineau, Hinarii Pichevin, Philippe Tann. One-Year Volatility of Reserve Risk in a Multivariate Framework. 2013. ⟨hal-00848492v2⟩