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Chapter 03 - Introduction In this chapter we study payments...

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FIN 3220A Actuarial Models I Actuarial Models I Chapter 3 Life Annuities FIN 3220A (2005-2006) Page 2 Chapter 3 Life Annuities Introduction Introduction In this chapter, we study payments contingent on survival, as provided by various forms of life annuities A life annuity is a series of payments made continuously or at equal intervals while a given life survives It may be temporary (limited to a given years) or for whole life The payment intervals may commence immediately or may be deferred Payments may be due at the beginnings of the payment intervals ( annuities-due ) or at the ends of such intervals ( annuities- immediate ) Life annuities play major role in life insurance operations, pension systems, and disability or worker’s compensation insurance FIN 3220A (2005-2006) Page 3 Chapter 3 Life Annuities Continuous Life Annuities Continuous Life Annuities Consider annuities payable continuously at the rate of 1 per year This is of course an abstraction A whole life annuity provides for payments until death The PV of annuity payments to be made is Here, T is the future lifetime of ( x ) for all 0 T a T = Y FIN 3220A (2005-2006) Page 4 Chapter 3 Life Annuities Continuous Life Annuities Continuous Life Annuities The distribution function of Y can be obtained from that for T as follows: ( ) ( ) ( ) ( ) ( ) ( ) ( ) Pr Pr Pr 1 Pr 1 ln 1 Pr ln 1 1 for 0 T T T T F y y a y v y v y y T y F y = = = ≤ δ = − δ − δ = δ − δ = < < δ δ Y Y
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