This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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: TwoStep Process for Pricing Premiums: 1) Find an expression for the lossatissue 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 hpayment 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 nyear endow ment insurance of 1 on (x)....
View
Full
Document
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
 Staff
 Formulas

Click to edit the document details