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Time-Consistent Actuarial Valuations

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  • Antoon Pelsser

Abstract

Recent theoretical results establish that time-consistent valuations (i.e. pricing operators) can be created by backward iteration of one-period valuations. In this paper we investigate the continuous-time limits of well-known actuarial premium principles when such backward iteration procedures are applied. We show that the one-period variance premiumprinciple converges to the non-linear exponential indifference valuation. Furthermore, we study the convergence of the one-period standard-deviation principle and establish that the Cost-of-Capital principle, which is widely used by the insurance industry, converges to the same limit as the standard-deviation principle. Finally, we study the connections between our time-consistent pricing operators, Good Deal Bound pricing and pricing under model ambiguity.

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  • Antoon Pelsser, 2011. "Time-Consistent Actuarial Valuations," Papers 1109.1751, arXiv.org.
    • Handle: RePEc:arx:papers:1109.1751
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    5. Balter, Anne G. & Pelsser, Antoon, 2020. "Pricing and hedging in incomplete markets with model uncertainty," European Journal of Operational Research, Elsevier, vol. 282(3), pages 911-925.
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    7. van Bilsen, Servaas & Linders, Daniël, 2019. "Affordable and adequate annuities with stable payouts: Fantasy or reality?," Insurance: Mathematics and Economics, Elsevier, vol. 86(C), pages 19-42.
    8. Ketelbuters, John John & Hainaut, Donatien, 2021. "Time-Consistent Evaluation of Credit Risk with Contagion," LIDAM Discussion Papers ISBA 2021004, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    9. Delong, Łukasz & Dhaene, Jan & Barigou, Karim, 2019. "Fair valuation of insurance liability cash-flow streams in continuous time: Theory," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 196-208.

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