13_AS_9_lec_a

Developments the standardized mortality ratio 1

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Unformatted text preview: Module 9: Standardization and new developments The standardized mortality ratio 1 Introduction: Single Index Approach 2 Crude Mortality rate 3 Directly standardized mortality rate 4 Indirectly Standardized Mortality Rate 5 The standardized mortality ratio 6 More advanced mortality models 14/15 Actuarial Statistics – Module 9: Standardization and new developments The standardized mortality ratio The standardized mortality ratio The standardised mortality ration is defined as the indirectly standardized mortality rate the crude mortality rate in the standard population sEc sm x ,t x ,t x x = c Ex ,t s mx ,t x x = 14/15 sEc x ,t c Ex ,t mx ,t ÷ x sEc sm x ,t x ,t x sEc x ,t = c Ex , t m x , t cs x Ex , t m x , t x Actual Deaths in population Expected deaths in population using standard mortality A value of the ratio less than 1 indicates a population with mortality lighter than in the standard population. A value of the ratio greater than 1 indicates a population with mortality heavier than in the standard population. Actuarial Statistics – Module 9: Standardization and new developments More advanced mortality models 1 Introduction: Single Index Approach 2 Crude Mortality rate 3 Directly standardized mortality rate 4 Indirectly Standardized Mortality Rate 5 The standardized mortality ratio 6 More advanced mortality models 15/15 Actuarial Statistics – Module 9: Standardization and new developments More advanced mortality models Lee-Carter model Lee, R., and L. Carter (1992) Modelling and Forecasting US mortality (J Amer. Stat. Assoc) Time series based model to forecast mortality Considers the central death rate m (x , t ) Model is ln (m (x , t )) = a (x ) + b (x ) k (t ) + ε (x , t ) Their work started a large amount of research for “stochastic mortality modeling” 15/15...
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