Lee-Carter mortality forecasting: methodological and computational issues.
[Tesi di dottorato]
In this thesis we describe relevant aspects of the development of survival modelling in actuarial mathematics. In particular we introduce some recent mortality projection models and research dealing with uncertainty in future trends and we review the relevant actuarial evidence. We then investigate the feasibility of using the Lee-Carter methodology to construct mortality forecasts for the Italian population. We fit the model to the matrix of Italian death rates for each gender from 1950 to 2000. A time-varying index of mortality is forecasted in an ARIMA framework and is used to generate projected life tables. In particular we focus on life expectancies at birth and, for the purpose of comparison, we introduce an alternative approach for forecasting life expectancies on a period basis. The resulting forecasts generated by the two methods are then compared. We also analyse, in a Lee Carter mortality context, the standard endowment policy under a fair value approach. In order to determine an actuarial model for the fair valuation of the stochastic stream of cash flows at time t, we base our demographic assumptions on the life and death probabilities extracted from the tables constructed using the Lee Carter model. The emphasis of the existing literature has been on financial markets; the primary feature of our model is its focus on the demographic reference system.
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