Comment on

1
Comment on Modeling the Forward Surface of
Mortality

• Discussant Jack C. Yue National Chengchi
  University September 26, 2009

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About the paper

• Modeling the Forward Surface of Mortality
• ?D. Bauer, F. E. Benth, and R. Kiesel
• This is an interesting paper and I will focus on
  the following two questions
• ?Practical issues
• ?More Examples

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Forward Force Models

• This paper provides an interesting history about
  the annuity, and a detailed theoretical
  development of forward force models.
• This paper focuses on the implicit risk of
  employing mortality forecast, not on the
  mortality forecast itself.
• ?Consistency problem of parametric forward models
  
• ?Existence of finite dimensional realizations for
  Guassian forward models

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Cohort vs. Period Life Tables

• For the projection of mortality rates, the data
  are usually collected in the age-specific format.
• ?For example, the famous Lee-Carter model uses
  annual mortality data and can be treated as a
  special case of age-period-cohort model,
• where the subscripts x and t represent the age
  and time (period) effects, respectively.

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Mortality Rates in Cohort and Period Life Tables
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Spot Force Mortality Models

• Most stochastic models use the mortality of all
  ages in a single year, instead of dealing with
  mortality rates in all ages for a cohort.
• Need to project the future values parameters in
  order to obtain the future mortality rates.
• ?In the Lee-Carter model, time series analysis
  (ARIMA) is applied on the parameter ?t.
• ?For the Gompertz Law , we
  need to find the future values of Bt and Ct.

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Spot Force Mortality Models (cont.)

• As the author said, the most obvious approach is
  to replace constant parameters in spot force
  mortality models by stochastic processes.
• ?For example, the authors use the Gompertz law as
  an example to demonstrate the forward force
  mortality models.

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Suggestions

• We need demonstration on how to use the proposed
  model to compute the annuity value.
• ?e.g., How to determine the values of parameters
  in the Gompertz Law, and the future mortality
  rates.
• How do we apply the forward force models?
• ?e.g., How do we choose a feasible model among
  all possible candidates and by what kind of
  criterion (or criteria)?

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Suggestions (cont.)

• In addition to theoretical developments,
  empirical or simulation results would help the
  readers to understand.
• ?e.g., Compare with the LC model, regarding
  errors in estimation and in prediction.
• Give more detailed explanations (and also more
  background knowledge) why the forward force model
  is better than the spot force models.

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Thank you for your attention!