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LONGEVITY 13 ： International Longevity Risk and Capital Markets Solutions Conference 2017

LONGEVITY 13 ： International Longevity Risk and Capital Markets Solutions Conference 2017. A Bayesian Method for Forecasting Mortality Rates by Health State: with Rising Life Expectancy. Atsuyuki Kogure Keio University, Japan Shinichi Kamiya Nanyang Technological University, Singapore

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LONGEVITY 13 ： International Longevity Risk and Capital Markets Solutions Conference 2017

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  1. LONGEVITY 13：International Longevity Risk and Capital Markets Solutions Conference 2017 A Bayesian Method for Forecasting Mortality Rates by Health State: with Rising Life Expectancy AtsuyukiKogure Keio University, Japan Shinichi Kamiya Nanyang Technological University, Singapore Takahiro Fushimi Stanford University, USA September 21-22, 2017

  2. Aging and mortality forecasting heavy burdens on long-term care cost

  3. Japan has been and will be agingvery fast ! Population Pyramid of Japan from 1920 to 2050

  4. Subpopulation mortality forecasting

  5. Our objectives

  6. Mortalityforecasting for total population Death numbers for age x at time t Exposures(populationsizes) for age x at time t Ext Dxt Force of mortality

  7. Subpopulations by health state Death numbers for age x at time tin state j Exposures(subpopulationsizes) for age x at time t in state j Health state 0 (no problem) Dxt0 Ext0 Ext1 Health state 1 (least severe) Dxt1 ．．． ．．． ．．． ExtJ Health state J (most severe) DxtJ

  8. Lee-Carter structure by health state

  9. Mortality forecasting for subpopulations

  10. Force of mortality for total population

  11. Mixture Lee-Carter model

  12. Identifiability of the mixture LC model

  13. Bayesian estimation: parameter uncertainty

  14. Priors for observation equation

  15. Priors for health factors

  16. Priors for State Equation

  17. Hyperparameters

  18. Application: Public Long-term Care Insurance System in Japan

  19. Japanese Public Long-term Care System

  20. Trends of Persons Certified As Requiring Long-term Care Total number of certified persons in 2015 is 608 (in 10, 000’s) increased by a factor of 2.79 for the past 15 years. total In 10,000’s Care levels Transitional Care levels Support levels 2000 2005 2010 2015 Source: Monthly Report on the Status of Long-term Care Insurance

  21. Health states

  22. Sizes of LTC subpopulations

  23. Bayes Computation: MCMC

  24. Posterior distributions forη，γ65，β65，κ2001: male η γ65 κ2001 β65

  25. Summary statistics of posterior distributions: male

  26. Changes in posterior means of γx，βx，κtover x or t γx βx κt male

  27. Posterior distributions for η，γ65，β65，κ2001: female η γ65 β65 κ2001

  28. Summary statistics of posterior distributions: female

  29. Chanes in posterior means ofγx， βx ，κtover x or t γx βx κt female

  30. Gender difference in health effects male ηj ｈealth effect femae j=health state

  31. Future mortality rates by health status

  32. Future mortality rates by health status ｊ=5 ｊ=4 ｊ=3 ｊ=2 ｊ=1 ｊ=0 Male Female

  33. Survival rates by health status

  34. Future survival rates by health status Male Female

  35. Conclusions (1)

  36. Conclusions (2)

  37. References

  38. References

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