On Stochastic Mortality Modeling

In the last decennium a vast literature on stochastic mortality models has been developed. All well-known models have nice features but also disadvantages. In this paper a stochastic mortality model is proposed that aims at combining the nice features from the existing models, while eliminating the disadvantages. More specifically, the model fits historical data very well, is applicable to a full age range, captures the cohort effect, has a non-trivial (but not too complex) correlation structure and has no robustness problems, while the structure of the model remains relatively simple. Also, the paper describes how to incorporate parameter uncertainty in the model. Furthermore, a risk neutral version of the model is given, that can be used for pricing.

[1]  Ronald Lee,et al.  Modeling and forecasting U. S. mortality , 1992 .

[2]  Kevin Dowd,et al.  A Two-Factor Model for Stochastic Mortality With Parameter Uncertainty: Theory and Calibration , 2006 .

[3]  PIET DE JONG,et al.  Extending Lee–Carter Mortality Forecasting , 2006 .

[4]  Steven Haberman,et al.  On simulation-based approaches to risk measurement in mortality with specific reference to Poisson Lee-Carter modelling , 2008 .

[5]  Steven Haberman,et al.  A cohort-based extension to the Lee-Carter model for mortality reduction factors , 2006 .

[6]  Kevin Dowd,et al.  Modelling and management of mortality risk: a review , 2008 .

[7]  M. Denuit,et al.  Stochastic Mortality Under Measure Changes , 2009 .

[8]  David Blake,et al.  A Quantitative Comparison of Stochastic Mortality Models Using Data From England and Wales and the United States , 2009 .

[9]  Andrew J. G. Cairns,et al.  A discussion of parameter and model uncertainty in insurance , 2000 .

[10]  Michel Denuit,et al.  A Poisson log-bilinear regression approach to the construction of projected lifetables , 2002 .

[11]  Steven Haberman,et al.  Lee–Carter mortality forecasting with age-specific enhancement , 2003 .

[12]  Paul H. C. Eilers,et al.  Smoothing and forecasting mortality rates , 2004 .

[13]  J. Maindonald,et al.  Applying Lee-Carter under conditions of variable mortality decline , 2002, Population studies.

[14]  Bayesian analysis of ARMA models using noninformative priors , 1995 .

[15]  A. Zellner.  Estimators for Seemingly Unrelated Regression Equations: Some Exact Finite Sample Results , 1963 .

[16]  Ronald Lee,et al.  Evaluating the performance of the lee-carter method for forecasting mortality , 2001, Demography.

[17]  M. Dahl,et al.  Stochastic mortality in life insurance: market reserves and mortality-linked insurance contracts , 2004 .

[18]  M. Milevsky,et al.  Mortality derivatives and the option to annuitise , 2001 .

[19]  M. Denuit,et al.  Smoothing the Lee–Carter and Poisson log-bilinear models for mortality forecasting , 2007 .

[20]  David F. Schrager.  Affine Stochastic Mortality , 2006 .

[21]  Ingrid Van Keilegom,et al.  Bootstrapping the Poisson log-bilinear model for mortality forecasting , 2005 .

[22]  R. C. Willets,et al.  The Cohort Effect: Insights and Explanations , 2004, British Actuarial Journal.

[23]  David Blake,et al.  Pricing Death: Frameworks for the Valuation and Securitization of Mortality Risk* , 2006, ASTIN Bulletin.