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Unformatted text preview: Name: Lecture Section Time: MATH 471: Actuarial Theory I Final Exam December 18, 2009 Exam Information and Instructions: There are 23 problems on this exam for a total of 90 points. In every problem, keep at least six decimal places during your calculations and refer to the accompanying tables when necessary. Furthermore: Problems 1 - 20 are multiple choice, worth 3 points each. • For each of these problems, circle the letter that corresponds to your answer choice IN THIS EXAM. The 16 page exam booklet is for scratch work only and will NOT be considered in the grading of this exam. • There is only one correct answer per problem. • In some problems, answer choices are rounded. Circle the letter of the answer choice that is closest to your own answer. • No partial credit will be awarded for any of these problems. Problems 21 - 23 are written answer, worth 10 points each. • For each of these problems, calculate your answer in the space provided after each problem IN THIS EXAM. The 16 page exam booklet is for scratch work only and will NOT be considered in the grading of this exam. • Partial credit can be earned for these problems, provided that you SHOW YOUR WORK. GOOD LUCK! 1. You are given: (i) L is the loss-at-issue random variable for a fully continuous 20-year endowment insurance of 1 on (50). (ii) ¯ A 50: 20 = 0.60 and 2 ¯ A 50: 20 = 0.40 (iii) δ = 0.04 (iv) Annual premiums are calculated using the equivalence principle. Calculate var ( L ). (A) 0.00 (B) 0.04 (C) 0.10 (D) 0.19 (E) 0.25 2. An individual can be in one of three possible states within a year: State 1 = active, State 2 = disabled, and State 3 = dead Transitions between states can only occur at the end of the year. The transition matrix, corresponding to a homogeneous Markov Chain, is: Q = . 7 0 . 2 0 . 1 . 3 0 . 5 0 . 2 1 Calculate the probability than an active individual at time 0 will be dis- abled at time 2....
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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.

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RelativeResourceManagere3 - Name: Lecture Section Time:...

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