This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Chapter 5 Life annuities Chapter 5 Life annuities ACTSC 232 Introduction to Actuarial Mathematics Tianxiang Shi Department of Statistics and Actuarial Science University of Waterloo Winter 2012 Tianxiang Shi([email protected]) Chapter 5 Life annuities Outline 1 Introduction 2 Annuities payable continuously 3 Annual life annuities 4 Annuities payable m times per year 5 Guaranteed annuities 6 Variable life annuities Tianxiang Shi([email protected]) Chapter 5 Life annuities Introduction Overview Annuity : a regular series of payments. e.g. mortgage, pensions . Annuity certain : the amount, the number and the timing of the payments are fixed, not contingent on any other factors. Life annuity : the number, the amount and the timing of the payments, at least one of them , depend on the survival of a life Annuity type: annuitydue : payments made at the beginning of each time unit. annuityimmediate : payments made at the end of each time unit. Tianxiang Shi([email protected]) Chapter 5 Life annuities Introduction Annuity certain review Annuity due and immediate Tianxiang Shi([email protected]) Chapter 5 Life annuities Introduction Annuity certain review Annuity due and immediate ¨ a n (¨ a ( m ) n ) = 1 v n d ( d ( m ) ) , a n ( a ( m ) n ) = 1 v n i ( i ( m ) ) Continuous annuity ¯ a n = 1 v n δ Increasing annuity Tianxiang Shi([email protected]) Chapter 5 Life annuities Introduction Annuity certain review Annuity due and immediate ¨ a n (¨ a ( m ) n ) = 1 v n d ( d ( m ) ) , a n ( a ( m ) n ) = 1 v n i ( i ( m ) ) Continuous annuity ¯ a n = 1 v n δ Increasing annuity ( I ¨ a ) n (( Ia ) n , ( I ¯ a ) n ) = ¨ a n n · v n d ( i,δ ) , ( ¯ I ¯ a ) n = ¯ a n n · v n δ Decreasing annuity Tianxiang Shi([email protected]) Chapter 5 Life annuities Introduction Annuity certain review Annuity due and immediate ¨ a n (¨ a ( m ) n ) = 1 v n d ( d ( m ) ) , a n ( a ( m ) n ) = 1 v n i ( i ( m ) ) Continuous annuity ¯ a n = 1 v n δ Increasing annuity ( I ¨ a ) n (( Ia ) n , ( I ¯ a ) n ) = ¨ a n n · v n d ( i,δ ) , ( ¯ I ¯ a ) n = ¯ a n n · v n δ Decreasing annuity ( D ¨ a ) n (( Da ) n , ( D ¯ a ) n ) = n a n d ( i,δ ) , ( ¯ D ¯ a ) n = n ¯ a n δ Tianxiang Shi([email protected]) Chapter 5 Life annuities Annuities payable continuously Whole life continuous annuity Whole life continuous annuity of $ 1 per year A benefit of $ 1 per year is payable continuously, conditional on the survival of ( x ) to the payment dates. Y = Tianxiang Shi([email protected]) Chapter 5 Life annuities Annuities payable continuously Whole life continuous annuity Whole life continuous annuity of $ 1 per year A benefit of $ 1 per year is payable continuously, conditional on the survival of ( x ) to the payment dates....
View
Full
Document
This note was uploaded on 03/30/2012 for the course ACTSC 232 taught by Professor Matthewtill during the Winter '08 term at Waterloo.
 Winter '08
 MATTHEWTILL

Click to edit the document details