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ECONOMIC SCENARIO GENERATOR AND PARAMETER UNCERTAINTY: A BAYESIAN APPROACH

Published online by Cambridge University Press:  14 April 2019

Jean-François Bégin Open the ORCID record for Jean-François Bégin [Opens in a new window]
Jean-François Bégin*
Affiliation:
Department of Statistics and Actuarial ScienceSimon Fraser University8888 University Drive, Burnaby British Columbia, V5A 1S6, Canada E-mail: [email protected]
*
E-mail: [email protected]
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Abstract

In this article, we study parameter uncertainty and its actuarial implications in the context of economic scenario generators. To account for this additional source of uncertainty in a consistent manner, we cast Wilkie’s four-factor framework into a Bayesian model. The posterior distribution of the model parameters is estimated using Markov chain Monte Carlo methods and is used to perform Bayesian predictions on the future values of the inflation rate, the dividend yield, the dividend index return and the long-term interest rate. According to the US data, parameter uncertainty has a significant impact on the dispersion of the four economic variables of Wilkie’s framework. The impact of such parameter uncertainty is then assessed for a portfolio of annuities: the right tail of the loss distribution is significantly heavier when parameters are assumed random and when this uncertainty is estimated in a consistent manner. The risk measures on the loss variable computed with parameter uncertainty are at least 12% larger than their deterministic counterparts.

Keywords

Parameter uncertaintyeconomic scenario generatorBayesian inferenceMarkov Chain Monte Carlorisk
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 49 , Issue 2 , May 2019 , pp. 335 - 372
Copyright
Copyright © Astin Bulletin 2019 

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References

Ahlgrim, K.C., D’Arcy, S.P. and Gorvett, R.W. (2004) Modeling of economic series coordinated with interest rate scenarios. Technical report, Casualty Actuarial Society and the Society of Actuaries.Google Scholar
Ahlgrim, K.C., D’Arcy, S.P., and Gorvett, R.W. (2008) A comparison of actuarial financial scenario generators. Variance 2, 111–134.Google Scholar
Bernardo, J.M. and Smith, A.F. (2001) Bayesian Theory. New York, NY, USA: Wiley.Google Scholar
Bégin, J.-F. (2016) Deflation risk and implications for life insurers. Risks, 4, 46.CrossRefGoogle Scholar
Cairns, A.J. (2000) A discussion of parameter and model uncertainty in insurance. Insurance: Mathematics and Economics, 27, 313–330.Google Scholar
Cairns, A.J., Blake, D. and Dowd, K. (2006) A two-factor model for stochastic mortality with parameter uncertainty: theory and calibration. Journal of Risk and Insurance, 73, 687–718.CrossRefGoogle Scholar
Chan, T. (1998) Some applications of Lévy processes to stochastic investment models for actuarial use. ASTIN Bulletin, 28, 77–93.CrossRefGoogle Scholar
Chan, W.-S. (2002) Stochastic investment modelling: a multiple time-series approach. British Actuarial Journal, 8, 545–591.CrossRefGoogle Scholar
Chan, W.-S., Wong, A.C. and Tong, H. (2004) Some nonlinear threshold autoregressive time series models for actuarial use. North American Actuarial Journal, 8, 37–61.CrossRefGoogle Scholar
Fellingham, G.W., Kottas, A. and Hartman, B.M. (2015) Bayesian nonparametric predictive modeling of group health claims. Insurance: Mathematics and Economics, 60, 1–10.Google Scholar
Fisher, I. (1930) The Theory of Interest. New York, NY, USA: The Macmillan Co.Google Scholar
Gelman, A. and Rubin, D.B. (1992) Inference from iterative simulation using multiple sequences. Statistical Science, 7, 457–472.CrossRefGoogle Scholar
Geoghegan, T., Clarkson, R., Feldman, K., Green, S., Kitts, A., Lavecky, J., Ross, F., Smith, W. and Toutounchi, A. (1992) Report on the Wilkie stochastic investment model. Journal of the Institute of Actuaries, 119, 173–228.CrossRefGoogle Scholar
Gill, J. and Freeman, J.R. (2013) Dynamic elicited priors for updating covert networks. Network Science, 1, 68–94.CrossRefGoogle Scholar
Hartman, B.M. and Groendyke, C. (2013) Model selection and averaging in financial risk management. North American Actuarial Journal, 17, 216–228.CrossRefGoogle Scholar
Hartman, B.M. and Heaton, M.J. (2011) Accounting for regime and parameter uncertainty in regime-switching models. Insurance: Mathematics and Economics, 49, 429–437.Google Scholar
Hartman, B.M., Richardson, R. and Bateman, R. (2017) Parameter uncertainty. Technical report, Casualty Actuarial Society, Canadian Institute of Actuaries, and Society of Actuaries Report.Google Scholar
Hastings, W.K. (1970) Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57, 97–109.CrossRefGoogle Scholar
Hayne, R.M. (1999) Modeling parameter uncertainty in cash flow projections. In CAS Forum, pp. 133–151.Google Scholar
Heckman, P.E. and Meyers, G.G. (1983) The calculation of aggregate loss distributions from claim severity and claim count distributions. Proceedings of the Casualty Actuarial Society, 70, 22–61.Google Scholar
Huber, P. (1997) A review of Wilkie’s stochastic asset model. British Actuarial Journal, 3, 181–210.CrossRefGoogle Scholar
Marceau, E. and Gaillardetz, P. (1999) On life insurance reserves in a stochastic mortality and interest rates environment. Insurance: Mathematics and Economics, 25, 261–280.Google Scholar
Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H. and Teller, E. (1953) Equation of state calculations by fast computing machines. Journal of Chemical Physics, 21, 1087–1092.CrossRefGoogle Scholar
Meyers, G. and Schenker, N. (1983) Parameter uncertainty in the collective risk model. PCAS LXX, p. 111.Google Scholar
Nolde, N. and Parker, G. (2014) Stochastic analysis of life insurance surplus. Insurance: Mathematics and Economics, 56, 1–13.Google Scholar
O’Hagan, A. (1998) Eliciting expert beliefs in substantial practical applications. Journal of the Royal Statistical Society: Series D (The Statistician), 47, 21–35.Google Scholar
Pedersen, H., Campbell, M.P., Christiansen, S.L., Cox, S.H., Finn, D., Griffin, K., Hooker, N., Lightwood, M., Sonlin, S.M. and Suchar, C. (2016) Economic scenario generators: a practical guide. Technical report, Society of Actuaries.Google Scholar
Pflaumer, P. (2011) Methods for estimating selected life table parameters using the Gompertz distribution. In Proceedings of the Joint Statistical Meetings, Social Statistics Section, Miami Beach, pp. 733–747.Google Scholar
Redington, F.M. (1952) Review of the principles of life-office valuations. Journal of the Institute of Actuaries, 78, 286–340.CrossRefGoogle Scholar
Sahin, S., Cairns, A. and Kleinow, T. (2008) Revisiting the Wilkie investment model. In 18th International AFIR Colloquium, Rome, pp. 1–24.Google Scholar
Sherris, M., Tedesco, L. and Zehnwirth, B. (1997) Stochastic investment models: unit roots, cointegration, state space and GARCH models. In Actuarial Research Clearing House, Vol. 1, pp. 95–144.Google Scholar
Upton, G. and Cook, I. (2014) A Dictionary of Statistics. New York: Oxford University Press.Google Scholar
Whitten, S. and Thomas, R.G. (1999) A non-linear stochastic asset model for actuarial use. British Actuarial Journal, 5, 919–953.CrossRefGoogle Scholar
Wilkie, A., Sahin, S., Cairns, A. and Kleinow, T. (2011) Yet more on a stochastic economic model, part 1: updating and refitting, 1995 to 2009. Annals of Actuarial Science, 5, 53–99.CrossRefGoogle Scholar
Wilkie, A.D. (1986) A stochastic investment model for actuarial use. Transactions of the Faculty of Actuaries, 39, 341–403.CrossRefGoogle Scholar
Wilkie, A.D. (1995) More on a stochastic asset model for actuarial use. British Actuarial Journal, 1, 777–964.CrossRefGoogle Scholar
Wilkie, A.D. and Sahin, S. (2016) Yet more on a stochastic economic model: part 2: initial conditions, select periods and neutralising parameters. Annals of Actuarial Science, 10, 1–51.CrossRefGoogle Scholar
Wilkie, A.D. and Sahin, S. (2017 a) Yet more on a stochastic economic model: part 3A: stochastic Interpolation: Brownian and Ornstein–Uhlenbeck (OU) Bridges. Annals of Actuarial Science, 11, 74–99.CrossRefGoogle Scholar
Wilkie, A.D. and Sahin, S. (2017 b) Yet more on a stochastic economic model: part 3B: stochastic bridging for retail prices and wages. Annals of Actuarial Science, 11, 100–127.CrossRefGoogle Scholar
Wilkie, A.D. and Sahin, S. (2017 c) Yet more on a stochastic economic model: part 3C: stochastic bridging for share yields and dividends and interest rates. Annals of Actuarial Science, 11, 128–163.CrossRefGoogle Scholar
Wilkie, A.D. and Sahin, S. (2018) Yet more on a stochastic economic model: part 4: a model for share earnings, dividends, and prices. Annals of Actuarial Science, 12, 67–105.CrossRefGoogle Scholar
Zhang, L., Mykland, P.A. and At-Sahalia, Y. (2005) A tale of two time scales. Journal of the American Statistical Association, 100, 1394–1411.CrossRefGoogle Scholar
Zhang, S., Hardy, M. and Saunders, D. (2018) Updating Wilkie’s economic scenario generator for U.S. applications. North American Actuarial Journal, 22, 600–622.CrossRefGoogle Scholar
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