A computationally efficient algorithm for estimating the distribution of future annuity values under interest-rate and longevity risks. (English) Zbl 1228.91031

Summary: This paper proposes a computationally efficient algorithm for quantifying the impact of interestrate risk and longevity risk on the distribution of annuity values in the distant future. The algorithm simulates the state variables out to the end of the horizon period and then uses a Taylor series approximation to compute approximate annuity values at the end of that period, thereby avoiding a computationally expensive “simulation-within-simulation” problem. Illustrative results suggest that annuity values are likely to rise considerably but are also quite uncertain. These findings have some unpleasant implications both for defined contribution pension plans and for defined benefit plan sponsors considering using annuities to hedge their exposure to these risks at some point in the future.


91B30 Risk theory, insurance (MSC2010)
91G30 Interest rates, asset pricing, etc. (stochastic models)
62P05 Applications of statistics to actuarial sciences and financial mathematics
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[1] Benjamin B., The Analysis of Mortality and Other Actuarial Statistics., 3. ed. (1993)
[2] Blake D., British Actuarial Journal 12 pp 153– (2006)
[3] Cairns A. J. G., Interest Rate Models: An Introduction (2004) · Zbl 1140.91039
[4] Cairns A. J. G., Modelling and Management of Longevity Risk: Approximations to Survivor Functions and Dynamic Hedging (2011) · Zbl 1230.91068
[5] Cairns A. J. G., Journal of Risk and Insurance 73 pp 687– (2006)
[6] Cairns A. J. G., Astin Bulletin 36 pp 79– (2006) · Zbl 1162.91403
[7] Cairns A. J. G., North American Actuarial Journal 13 (1) pp 1– (2009)
[8] Cox J. C., Econometrica 53 pp 385– (1985) · Zbl 1274.91447
[9] Finkelstein A., Economic Journal 112 pp 28– (2002)
[10] Perks W., Journal of the Institute of Actuaries 63 pp 12– (1932)
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