Stochastic Mortality Models
Fitting mortality rates and hence longevity risk quantification dynamically continues to be a challenge especially in the developing countries. Earlier development relied on one-factor model by Lee and Carter (1992). Lee and Carter model is widely applied since it has been found to provide fairly accurate estimations and population projections for both the academicians and practitioners. Later on, Renshaw and Haberman and Halzoupoiz(1996) and Renshaw and Heberma (2003) analysed the Lee-Carter model and proposed a new model.
More recent works have develop a two factor model and considered the cohort effect in mortality modeling which Lee and Carter model lacked. For instance, Renshaw and Haberman (2003) applied …show more content…
Models based on the Lee- Carter model incorporating cohort effects have since been introduced for instance Renshaw and Haberman (2006).
Renshaw and Haberman (2003) Model
Renshaw and Haberman(2003) proposed a multifactor age-period model (2.7)
Where and are dependent period effects (for example a bivariate random walk).
The model offer significant advantages over the Lee- Carter model. However both fail to tackle the cohort effect. Renshaw and Haberman (2006) Cohort Model
The Renshaw- Haberman (2006) is an extended version of the Lee- Carter model with an extra parameter that gives the cohort effect to give . (2.8)
Where is the mortality is index in year t (random period effect) and is a random cohort effect that is a function of the years of birth t-x.
The parameters in the model are not fully identified and therefore the enforced are , . In their analysis of England and Wales data, Renshaw and Haberman found that there was a significant improvement over the Lee- Carter model. The most noticeable improvement was that an analysis of the standardized residuals revealed very little dependence on the year of
Fitting mortality rates and hence longevity risk quantification dynamically continues to be a challenge especially in the developing countries. Earlier development relied on one-factor model by Lee and Carter (1992). Lee and Carter model is widely applied since it has been found to provide fairly accurate estimations and population projections for both the academicians and practitioners. Later on, Renshaw and Haberman and Halzoupoiz(1996) and Renshaw and Heberma (2003) analysed the Lee-Carter model and proposed a new model.
More recent works have develop a two factor model and considered the cohort effect in mortality modeling which Lee and Carter model lacked. For instance, Renshaw and Haberman (2003) applied …show more content…
Models based on the Lee- Carter model incorporating cohort effects have since been introduced for instance Renshaw and Haberman (2006).
Renshaw and Haberman (2003) Model
Renshaw and Haberman(2003) proposed a multifactor age-period model (2.7)
Where and are dependent period effects (for example a bivariate random walk).
The model offer significant advantages over the Lee- Carter model. However both fail to tackle the cohort effect. Renshaw and Haberman (2006) Cohort Model
The Renshaw- Haberman (2006) is an extended version of the Lee- Carter model with an extra parameter that gives the cohort effect to give . (2.8)
Where is the mortality is index in year t (random period effect) and is a random cohort effect that is a function of the years of birth t-x.
The parameters in the model are not fully identified and therefore the enforced are , . In their analysis of England and Wales data, Renshaw and Haberman found that there was a significant improvement over the Lee- Carter model. The most noticeable improvement was that an analysis of the standardized residuals revealed very little dependence on the year of