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Lecture%201%20Annotated - Life Insurance and Superannuation...

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Life Insurance and Superannuation Models Week 1: Life Insurances (Single Life) February 24, 2011 1 / 23
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Week 1: Life Insurances (Single Life) Summary Life insurance. Benefits payable contingent upon death; payment made to a designated beneficiary. Actuarial present values ( APV ) Actuarial symbols and notation Insurance payable at the moment of death Continuous Level benefits, varying benefits (e.g. increasing, decreasing) Insurances payable at the end of year of death Discrete Level benefits, varying benefits (e.g. increasing, decreasing) References Chapter 4 (Bowers, et al.) or Chapter 3 (Gerber) ACTL3002: Week 1 2
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Life Insurance Contracts Made between a life insurance company and one or more persons called the policyholders Policyholders agrees to pay an amount or series of amounts to the life insurance company called premiums. In return the life insurance company agrees to pay an amount or amounts called benefit(s), to the policyholder on the occurrence of a specific event. Benefits payable under two main types: On or following the death of the policyholder, Payable provided the life survives for a given term e.g. annuity. ACTL3002: Week 1 3
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Types of Life Insurance Contracts Whole life insurance contract Benefits are paid on the policyholder’s death Term assurance contract A contract to pay a sum assured on or after death provided death occurs during a specified period, called the term of the contract. Pure endowment contract Provides a sum assured at the end of a fixed term, provided the policyholder is then alive. An endowment contract This is a combination of a term assurance and a pure endowment assurance. ACTL3002: Week 1 4
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The Present Value Random Variable Denote by Z , the present value random variable. This gives the value, at policy issue, of the benefit payment. In the case where the benefit is payable at the moment of death, Z clearly depends on the time-until-death T . It is Z = b T v T where: b T is called the benefit payment function. v T is the discount function. ACTL3002: Week 1 5
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Fixed Term Life Insurance An n -year term life insurance provides payment if the insured dies within n years from issue. For a unit of benefit payment we have b T = braceleftbigg 1 , T n 0 , T > n and v T = v T .
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