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INSURANCE VALUATION: A TWO-STEP GENERALISED REGRESSION APPROACH

Published online by Cambridge University Press:  03 December 2021

Karim Barigou Open the ORCID record for Karim Barigou [Opens in a new window] ,
Valeria Bignozzi  and
Andreas Tsanakas
Karim Barigou*
Affiliation:
Univ Lyon, Université Claude Bernard Lyon 1, Laboratoire de Sciences Actuarielle et Financière, Institut de Science Financière et d’Assurances (50 Avenue Tony Garnier, F-69007 Lyon, France) E-Mail: karim.barigou@univ-lyon1.fr
Valeria Bignozzi
Affiliation:
Department of Statistics and Quantitative Methods University of Milano-Bicocca 20126 Milan, Italy E-Mail: valeria.bignozzi@unimib.it
Andreas Tsanakas
Affiliation:
Bayes Business School City, University of LondonLondon EC1V 0HB, UK E-Mail: a.tsanakas.1@city.ac.uk
*
E-Mail: karim.barigou@univ-lyon1.fr
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Abstract

Current approaches to fair valuation in insurance often follow a two-step approach, combining quadratic hedging with application of a risk measure on the residual liability, to obtain a cost-of-capital margin. In such approaches, the preferences represented by the regulatory risk measure are not reflected in the hedging process. We address this issue by an alternative two-step hedging procedure, based on generalised regression arguments, which leads to portfolios that are neutral with respect to a risk measure, such as Value-at-Risk or the expectile. First, a portfolio of traded assets aimed at replicating the liability is determined by local quadratic hedging. Second, the residual liability is hedged using an alternative objective function. The risk margin is then defined as the cost of the capital required to hedge the residual liability. In the case quantile regression is used in the second step, yearly solvency constraints are naturally satisfied; furthermore, the portfolio is a risk minimiser among all hedging portfolios that satisfy such constraints. We present a neural network algorithm for the valuation and hedging of insurance liabilities based on a backward iterations scheme. The algorithm is fairly general and easily applicable, as it only requires simulated paths of risk drivers.

Keywords

Market-consistent valuationquantile regressionSolvency IIcost-of-capitaldynamic risk measurement
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 52 , Issue 1 , January 2022 , pp. 211 - 245
Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of The International Actuarial Association

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