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Mean reversion in stochastic mortality: why and how? (English) Zbl 1455.91231

Summary: Life insurance companies use stochastic models to forecast mortality. According to the literature, non-mean reversion models are more suitable for mortality modelling than mean reversion models with a fixed long-term target. In this paper, we adopt stochastic affine processes for the force of mortality and study the impact of adding a time-dependent long-term mean reversion level to two non-mean-reverting processes. We calibrate the models to different generations of the Belgian population and assess these models’ abilities to predict mortality using different statistical methodologies. The backtest shows that the survival curves provided by the mean-reverting processes are closer to reality. Thus, we conclude that incorporating a time-dependent target into these considered models improves their performance significantly.

MSC:

91G05 Actuarial mathematics
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
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[1] Apicella, G.; Dacorogna, M.; Lorenzo, ED; Sibillo, M., Improving the forecast of longevity by combining models, N Am Actuar J, 23, 298-319 (2019) · Zbl 1410.91253
[2] Biffis, E., Affine processes for dynamic mortality and actuarial valuations, Insur Mathe Econ, 37, 443-468 (2005) · Zbl 1129.91024
[3] Cairns, AJ; Blake, D.; Dowd, K., Pricing deaths: frameworks for the valuation and securitisation of mortality risk, ASTIN Bull, 36, 79-120 (2006)
[4] Cairns, AJ; Blake, D.; Dowd, K., A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration, J Risk Insur, 73, 687-718 (2006)
[5] Cox, JC; Ingersoll, JE Jr; Ross, SA, An intertemporal general equilibrium model of asset prices, Econom J Econom Soc, 20, 363-384 (1985) · Zbl 0576.90006
[6] Dahl, M., Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts, Insur Math Econ, 35, 113-136 (2004) · Zbl 1075.62095
[7] Denuit M, Devolder P (2006) Continuous time stochastic mortality and securitization of longevity risk. Technical report, Working Paper UCL 06-02
[8] Duffie, D.; Filipovic, D.; Schachermayer, W., Affine processes and applications in finance, Anna Appl Probabi, 20, 984-1053 (2003) · Zbl 1048.60059
[9] Duffie, D.; Pan, J.; Singleton, K., Transform analysis and asset pricing for affine jump-diffusion, Econometrica, 68, 1343-1376 (2000) · Zbl 1055.91524
[10] Hull, JC, Options, futures, and other derivatives (2009), Upper Saddle River: Pearson Prentice Hall, Upper Saddle River
[11] Kac, M., On distributions of certain wiener functionals, Trans Am Math Soc, 65, 1-13 (1949) · Zbl 0032.03501
[12] Lee, RD; Carter, LR, Modeling and forecasting US mortality, J Am Stat Assoc, 20, 20 (1992)
[13] Luciano E, Vigna E (2015) Non mean reverting affine processes for stochastic mortality ICER Working Papers
[14] Milevsky, M.; Promislow, S., Mortality derivatives and the option to annuitise, Insur Math Econ, 20, 20 (2001) · Zbl 1074.62530
[15] Mishura, Y.; Posashkova, S., Positivity of solution of nonhomogeneous stochastic differential equation with non-Lipschitz diffusion, Theory Stoch Processes, 14, 20 (2008)
[16] Schrager, D., Affine stochastic mortality, Insur Math Econ, 20, 22 (2006)
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