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FAIR VALUATION OF INSURANCE LIABILITY CASH-FLOW STREAMS IN CONTINUOUS TIME: APPLICATIONS

Published online by Cambridge University Press:  10 April 2019

Łukasz Delong ,
Jan Dhaene  and
Karim Barigou
Łukasz Delong*
Affiliation:
Warsaw School of Economics SGH Collegium of Economic Analysis, Institute of Econometrics Niepodległości162, Warsaw 02-554, Poland E-mail: lukasz.delong@sgh.waw.pl
Jan Dhaene
Affiliation:
KU Leuven Actuarial Research Group, AFI, Faculty of Business and Economics Naamsestraat 69, 3000 Leuven, Belgium E-mail: jan.dhaene@kuleuven.be
Karim Barigou
Affiliation:
KU Leuven Actuarial Research Group, AFI, Faculty of Business and Economics Naamsestraat 69, 3000 Leuven, Belgium E-mail: karim.barigou@kuleuven.be
*
E-mail: lukasz.delong@sgh.waw.pl
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Abstract

Delong et al. (2018) presented a theory of fair (market-consistent and actuarial) valuation of insurance liability cash-flow streams in continuous time. In this paper, we investigate in detail two practical applications of our theory of fair valuation. In the first example, we consider the fair valuation of a terminal benefit which is contingent on correlated tradeable and non-tradeable financial risks. In the second example, we consider a portfolio of unit-linked contracts contingent on a non-tradeable insurance and a tradeable financial risk. We derive partial differential equations (PDEs) which characterize the continuous-time fair valuation operators in these two examples and we find explicit solutions to these PDEs. The fair values of the liabilities are decomposed into the best estimate of the liability and a risk margin. The arbitrage-free representations of the fair values of the liabilities are derived and the dynamic hedging strategies associated with the continuous-time fair valuation operators are also established. Detailed interpretations of the results, which should be useful both for researchers and practitioners, are provided.

Keywords

Optimal quadratic hedgingactuarial valuationmarket-consistent valuationpartial differential equationbest estimaterisk marginnet asset value
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 49 , Issue 2 , May 2019 , pp. 299 - 333
Copyright
Copyright © Astin Bulletin 2019 

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