Math 472 Spring 2011 Chapter 10 Lecture Examples

# Math 472 Spring - MATH 472/567 Actuarial Theory II/Topics in Actuarial Theory I Chapter 10 Lecture Examples 1 Consider a double decrement model

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MATH 472/567: Actuarial Theory II/Topics in Actuarial Theory I Chapter 10: Lecture Examples 1. Consider a double decrement model with: (i) μ (1) x ( t ) = 2 25 for t 0 (ii) μ (2) x ( t ) = 7 25 for t 0 Determine: (a) The joint pdf of J and T . (b) The marginal probability functions for J and T . (c) The probability that (x) decrements due to cause 2 given decrement occurs at t = 1. (d) The expected time-until-decrement given that the cause-of-decrement is j = 2. 1

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2. For a double decrement model on (x): (i) μ (1) x ( t ) = t 50 for t 0 (ii) μ (2) x ( t ) = 2 t 50 for t 0 Calculate the probability that (x) will decrement due to cause 1. 2
3. Consider the double decrement model in Example 1. Calculate the probability that (x) decrements due to cause 2 during the ﬁfth year. 3

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4. Example 10.3.1 in the text. Assume l ( τ ) 65 = 1000. Fill in the missing entries of the following double decrement life table: x q ( 1 ) x q ( 2 ) x q ( τ ) x l ( τ ) x d ( 1 ) x d ( 2 ) x 65 0.02 0.05 66 0.03 0.06 67 0.04 0.07 68 0.05 0.08 69 0.06 0.09 70 0 1 4
5. Using the completed double decrement life table in Example 4, calculate: (a) 2 p ( τ ) 65 (b) 2 | q (1) 66 (c) 2 q (2) 67 5

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6. Students writing actuarial exams for the SOA face two decrements:
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## This note was uploaded on 05/18/2011 for the course MATH 472 taught by Professor Zhu during the Spring '08 term at University of Illinois, Urbana Champaign.

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Math 472 Spring - MATH 472/567 Actuarial Theory II/Topics in Actuarial Theory I Chapter 10 Lecture Examples 1 Consider a double decrement model

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