Two-step financial and actuarial valuations: Axiomatic characterization and applications

Two-step financial and actuarial valuations: Axiomatic characterization and applications

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Insurance liabilities are in most cases a combination of financial and actuarial risks. Determining the valuation of such payoffs requires combining standard actuarial valuations based on historical data with the financial information provided by market prices. In this paper, we present two broad classes of valuations: two-step financial valuations that are market-consistent and two-step actuarial valuations that are actuarial-consistent. We provide a complete axiomatic characterization for the two-step valuations based on coherent valuations. We also study the impact of the dependency structure between financial and actuarial risks on the fair valuation of insurance liabilities.

[1] Dhaene, J., Stassen, B., Barigou, K., Linders, D. and Chen, Z. (2017), “Fair valuation of insurance liabilities: merging actuarial judgement and market-consistency.” Insurance: Mathematics and Economics, vol. 76, pp. 14-27.

[2] Pelsser, A. and Stadje, M (2014), “Time-Consistent and Market-Consistent Evaluations.” Mathematical Finance, vol. 24(1), pp. 25-65.

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