On the Lifetime and One-Year Views of Reserve Risk, with Application to IFRS 17 and Solvency II Risk Margins

31 Pages Posted: 15 Mar 2018 Last revised: 30 May 2019

See all articles by Peter England

Peter England

City University London - Sir John Cass Business School

R. J. Verrall

City University London - Sir John Cass Business School

Mario V. Wuthrich

RiskLab, ETH Zurich

Date Written: March 16, 2018

Abstract

This paper brings together analytic and simulation-based approaches to reserve risk in general (P&C) insurance, applied to the traditional actuarial view of risk over the lifetime of the liabilities and to the one-year view of Solvency II. It also connects the lifetime and one-year views of risk. The framework of the model in Mack (1993) is used throughout, although the results have wider applicability.

The advantages of a simulation-based approach are highlighted, giving a full predictive distribution, which is used to estimate risk margins under Solvency II and risk adjustments under IFRS 17. We discuss methods for obtaining capital requirements in a cost-of-capital risk margin, and methods for estimating risk adjustments using risk measures applied to a simulated distribution of the outstanding liabilities over their lifetime.

Keywords: Stochastic Reserving, General Insurance, Bootstrap, Chain-Ladder, Prediction Error, Mean Square Error of Prediction, Cost-of-Capital, Risk Margin, Risk Adjustment, Solvency II, IFRS 17, Value-at-Risk, Tail Value-at-Risk, One-Year View, Proportional Hazards Transform, Coherent Risk Measure

Suggested Citation

England, Peter and Verrall, Richard J and Wuthrich, Mario V., On the Lifetime and One-Year Views of Reserve Risk, with Application to IFRS 17 and Solvency II Risk Margins (March 16, 2018). Available at SSRN: https://ssrn.com/abstract=3141239 or http://dx.doi.org/10.2139/ssrn.3141239

Peter England

City University London - Sir John Cass Business School ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

Richard J Verrall

City University London - Sir John Cass Business School ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

Mario V. Wuthrich (Contact Author)

RiskLab, ETH Zurich ( email )

Department of Mathematics
Ramistrasse 101
Zurich, 8092
Switzerland

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