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Unformatted text preview: MATH 471: Actuarial Theory I Final Exam: Formula Summary (Chapter 6 and Chapter 7 Part) This review sheet ONLY contains the key formulas from Chapters 6 and 7 of the text. You should refer to the review sheets for Midterms 1 and 2 for other key formulas. You should also refer to the text, notes, homework, etc. BENEFIT PREMIUMS: Two-Step Process for Pricing Premiums: 1) Find an expression for the loss-at-issue random variable (at time 0): L = PV(future benefits) - PV(future premiums) 2) Using the above L , calculate each premium using either: Equivalence Principle: E ( L ) = 0 = APV(future benefits) = APV(future premiums) at time 0, or Percentile Principle: Pr ( L > 0) = , where 0 < < 1. Premiums calculated via the equivalence principle are called benefit pre- miums . Premiums calculated via the percentile method are called 100 -th percentile premiums . Fully Continuous Premiums : Fully Continuous Life Insurance: a continuous life insurance on (x). The insurance is purchased with a continuous life annuity of annual premi- ums. Examples of fully continuous life insurances: Refer to Table 6.2.1. Note that in Table 6.2.1, benefit premiums are generally of the form: P ( A ) = A a . This is for a standard full payment insurance, where premiums are payable for the duration of the insurance coverage. Note the difference for h-payment insurance. 1 For a fully continuous whole life insurance of 1 on (x): var ( L ) = (1 + P ) 2 [ 2 A x- ( A x ) 2 ] A similar formula for var ( L ) applies to a fully continuous n-year endow- ment insurance of 1 on (x)....
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This note was uploaded on 02/14/2011 for the course MATH 471 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.
- Spring '08