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BIAS-CORRECTED INFERENCE FOR A MODIFIED LEE–CARTER MORTALITY MODEL

Published online by Cambridge University Press:  05 April 2019

Qing Liu ,
Chen Ling ,
Deyuan Li  and
Liang Peng
Qing Liu
Affiliation:
Department of Mathematical Statistics, School of Statistics and Research Center of Applied Statistics, Jiangxi University of Finance and Economics, Nanchang, Jiangxi 330013, P.R. China E-mail: [email protected]
Chen Ling
Affiliation:
Department of Risk Management and Insurance, Georgia State University, Atlanta, GA 30303, USA E-mail: [email protected]
Deyuan Li*
Affiliation:
Department of Statistics, School of Management, Fudan University, Shanghai 200433, P.R. China E-mail: [email protected]
Liang Peng
Affiliation:
Department of Risk Management and Insurance, Georgia State University, Atlanta, GA 30303, USA E-Mail: [email protected]
*
E-mail: [email protected]
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Abstract

As a benchmark mortality model in forecasting future mortality rates and hedging longevity risk, the widely employed Lee–Carter model (Lee, R.D. and Carter, L.R. (1992) Modeling and forecasting U.S. mortality. Journal of the American Statistical Association, 87, 659–671.) suffers from a restrictive constraint on the unobserved mortality index for ensuring model’s identification and a possible inconsistent inference. Recently, a modified Lee–Carter model (Liu, Q., Ling, C. and Peng, L. (2018) Statistical inference for Lee–Carter mortality model and corresponding forecasts. North American Actuarial Journal, to appear.) removes this constraint and a simple least squares estimation is consistent with a normal limit when the mortality index follows from a unit root or near unit root AR(1) model with a nonzero intercept. This paper proposes a bias-corrected estimator for this modified Lee–Carter model, which is consistent and has a normal limit regardless of the mortality index being a stationary or near unit root or unit root AR(1) process with a nonzero intercept. Applications to the US mortality rates and a simulation study are provided as well.

Keywords

AR(1) modelbias-corrected estimationLee–Carter mortality modelforecaststationaryunit rootC13C22C53
Type
Research Article
Information
ASTIN Bulletin: The Journal of the IAA , Volume 49 , Issue 2 , May 2019 , pp. 433 - 455
Copyright
Copyright © Astin Bulletin 2019 

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References

Biffis, E., Lin, Y. and Milidonis, A. (2017) The cross-section of Asia-Pacific mortality dynamics: Implications for longevity risk sharing. The Journal of Risk and Insurance, 84, 515–532.CrossRefGoogle Scholar
Chan, N.H. and Wei, C.Z. (1987) Asymptotic inference for nearly nonstationary AR(1) processes. The Annals of Statistics, 15, 1050–1063.CrossRefGoogle Scholar
Enchev, V., Kleinow, T. and Cairns, A.J.G. (2017) Multi-population mortality models: Fitting, forecasting and comparisons. Scandinavian Actuarial Journal, 4, 319–342.CrossRefGoogle Scholar
Hall, P. and Heyde, C. (1980) Martingale Limit Theory and Its Applications. New York: Academic Press.Google Scholar
Kwok, K.Y., Chiu, M.C. and Wong, H.Y. (2016) Demand for longevity securities under relative performance concerns: Stochastic differential games with cointegration. Insurance: Mathematics and Economics, 71, 353–366.Google Scholar
Lee, R.D. and Carter, L.R. (1992) Modeling and forecasting U.S. mortality. Journal of the American Statistical Association, 87, 659–671.Google Scholar
Leng, X. and Peng, L. (2016) Inference pitfalls in Lee-Carter model for forecasting mortality. Insurance: Mathematics and Economics, 70, 58–65.Google Scholar
Li, J., Chan, W. and Zhou, R. (2015) Semicoherent multipopulation mortality modeling: The impact on longevity risk securitization. The Journal of Risk and Insurance, 84, 1025–1065.CrossRefGoogle Scholar
Lin, Y., Shi, T. and Arik, A. (2017) Pricing buy-ins and buy-outs. The Journal of Risk and Insurance, 84, 367–392.CrossRefGoogle Scholar
Liu, Q., Ling, C. and Peng, L. (2018) Statistical inference for Lee-Carter mortality model and corresponding forecasts. North American Actuarial Journal, to appear.Google Scholar
Staudenmayer, J. and Buonaccorsi, J.P. (2005) Measurement error in linear autoregressive models. Journal of the American Statistical Association, 100, 841–852.CrossRefGoogle Scholar
Wong, T.W., Chiu, M.C. and Wong, H.Y. (2017) Managing mortality risk with longevity bonds when mortality rates are cointegrated. The Journal of Risk and Insurance, 84, 987–1023.CrossRefGoogle Scholar
Zhu, W.Tan, K. and Wang, C. (2017) Modeling multicountry longevity risk with mortality dependence: A Lévy subordinated hierarchical Archimedean copula approach. The Journal of Risk and Insurance, 84, 477–493.CrossRefGoogle Scholar