The fair valuation problem of guaranteed annuity options: The stochastic mortality environment case

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The fair value of guaranteed annuity options (2006, unknown): “For other proposals regarding the issue of stochastic mortality, see for example Milevsky and Promislow (2001), Ballotta and Haberman (2003a) or Dahl (2003).”
Analytical Calculation of Risk Measures for Variable Annuity Guaranteed Benefits (2012, background): “According to the strong law of large numbers, for a pool of N contracts of the same size with policyholders of age x at time 0 where N is large enough, there are approximately tpxN contracts still in force at time t.”
Mortality Risk Modeling: Applications to Insurance Securitization (2010, unknown): “(2006), Ballotta and Haberman (2006), Biffis and Millossovich (2006) and Bauer and Kramer (2007) focus on mortality risk as deviations from a trend. In those papers, the base trend may reflect mortality improvements, but longevity risk is not modeled explicitly. On the other hand, pension and annuit”
Mortality Regimes and Pricing (2011, background): “…different scenarios and uses various stochastic processes to model mortality and/or longevity risk (e.g. Milevsky and Promislow 2001; Dahl 2004; Ballotta and Haberman 2006; Cairns et al. 2006; Cox et al. 2006; Dahl and Møller 2006; Gründl et al. 2006; Lin and Cox 2008; Kogure and Kurachi 2010;…”