Huan Gao, Rogemar Mamon and Xiaoming Liu (2017), “Risk measurement of a guaranteed annuity option under a stochastic modelling framework”, Mathematics and Computers in Simulation, 132: 100-119. Huan Gao, Rogemar Mamon and Xiaoming Liu (2015), Pricing a guaranteed annuity option under correlated and regime-switching risk factors. European Actuarial Journal Volume 5, Issue 2, December 2015: 309--326. Huan Gao, Rogemar Mamon, Xiaoming Liu and Anton Tenyakov (2015), “A regime-switching framework for the valuation of guaranteed annuity options”, Insurance Mathematical and Economics, Vol. 63, issue C: 108-120. Xiaoming Liu, Rogemar Mamon and Huan Gao (2014), Pricing a guaranteed annuity option under stochastic mortality and financial risks: A change of probability measure approach. Stochastics. Vol. 86, No. 4, 594–608. Xiaoming Liu, Rogemar Mamon and Huan Gao (2013), A comonotonicity-based valuation method      for guaranteed annuity options. Journal of Computational and applied Mathematic 250 (2013): 58–69.  Xiaoming Liu (2013), Annuity uncertainty with stochastic mortality and interest rates. North American Actuarial Journal 17(2), 136–152. Xiaoming Liu and Sheldon Lin (2012), A subordinated Markov model for stochastic mortality.   European Actuarial Journal 2(1), 105-127. Xiaoming Liu, Jisoo Jang and Sun Mee Kim (2011). An application of comonotonicity theory in a stochastic life annuity framework. Insurance: Mathematics and Economics, 48, 271-279. Xiaoming Liu and John Braun (2010), Investigating Mortality Uncertainty Using the block bootstrap, Journal of Probability and Statistics, Volume 2010, 15 pages. Sheldon Lin and Xiaoming Liu (2007). Markov Aging Process and Phase-type Law of Mortality. North American Actuarial Journal, 11, 92-109. Xiaoming Liu and Hao Yu (2011), Assessing and extending the Lee-Carter model for long-term mortality prediction, 59 pages. SOA Living to 100 Symposium, Jan 5-7, 2011. 
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