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November2005ExamM（六）——北美精算师2014

来源：高顿网校 2014-07-23

　　以下为高顿网校小编给未来北美精算师们准备的November2005ExamM（六）——北美精算师2014。
　　30. For a fully discrete whole life insurance of 1000 on (45), you are given:

　　t 45 1000tV 45 t q +

　　22 235 0.015

　　23 255 0.020

　　24 272 0.025

　　Calculate 25 45 1000 V .

　　(A) 279

　　(B) 282

　　(C) 284

　　(D) 286

　　(E) 288

　　Exam M: Fall 2005 -31- GO ON TO NEXT PAGE

　　31. The graph of a piecewise linear survival function, ( ) s x , consists of 3 line segments with

　　endpoints (0, 1), (25, 0.50), (75, 0.40), (100, 0).

　　Calculate 15 20 55

　　55 35

　　q

　　q

　　.

　　(A) 0.69

　　(B) 0.71

　　(C) 0.73

　　(D) 0.75

　　(E) 0.77

　　Exam M: Fall 2005 -32- GO ON TO NEXT PAGE

　　32. For a group of lives aged 30, containing an equal number of smokers and non-smokers, you

　　are given:

　　(i) For non-smokers, ( ) 0.08 n x ? = , 30 x ≥

　　(ii) For smokers, ( ) 0.16, s x ? = 30 x ≥

　　Calculate 80 q for a life randomly selected from those surviving to age 80.

　　(A) 0.078

　　(B) 0.086

　　(C) 0.095

　　(D) 0.104

　　(E) 0.112

　　Exam M: Fall 2005 -33- GO ON TO NEXT PAGE

　　33. For a 3-year fully discrete term insurance of 1000 on (40), subject to a double decrement

　　model:

　　(i)

　　x ( )

　　x l τ ( ) 1

　　x d ( ) 2

　　x d

　　40 2000 20 60

　　41 ? 30 50

　　42 ? 40 ?

　　(ii) Decrement 1 is death. Decrement 2 is withdrawal.

　　(iii) There are no withdrawal benefits.

　　(iv) 0.05 i =

　　Calculate the level annual benefit premium for this insurance.

　　(A) 14.3

　　(B) 14.7

　　(C) 15.1

　　(D) 15.5

　　(E) 15.7

　　Exam M: Fall 2005 -34- GO ON TO NEXT PAGE

　　34. Each life within a group medical expense policy has loss amounts which follow a compound

　　Poisson process with 0.16 λ= . Given a loss, the probability that it is for Disease 1 is 1

　　16 .

　　Loss amount distributions have the following parameters:

　　Mean per loss

　　Standard

　　Deviation per loss

　　Disease 1 5 50

　　Other diseases 10 20

　　Premiums for a group of 100 independent lives are set at a level such that the probability

　　(using the normal approximation to the distribution for aggregate losses) that aggregate

　　losses for the group will exceed aggregate premiums for the group is 0.24.

　　A vaccine which will eliminate Disease 1 and costs 0.15 per person has been discovered.

　　Define:

　　A = the aggregate premium assuming that no one obtains the vaccine, and

　　B = the aggregate premium assuming that everyone obtains the vaccine and the cost of the

　　vaccine is a covered loss.

　　Calculate A/B.

　　(A) 0.94

　　(B) 0.97

　　(C) 1.00

　　(D) 1.03

　　(E) 1.06

　　Exam M: Fall 2005 -35- GO ON TO NEXT PAGE

　　35. An actuary for a medical device manufacturer initially models the failure time for a particular

　　device with an exponential distribution with mean 4 years.

　　This distribution is replaced with a spliced model whose density function:

　　(i) is uniform over [0, 3]

　　(ii) is proportional to the initial modeled density function after 3 years

　　(iii) is continuous

　　Calculate the probability of failure in the first 3 years under the revised distribution.

　　(A) 0.43

　　(B) 0.45

　　(C) 0.47

　　(D) 0.49

　　(E) 0.51

　　Exam M: Fall 2005 -36- GO ON TO NEXT PAGE

　　36. For a fully continuous whole life insurance of 1 on (30), you are given:

　　(i) The force of mortality is 0.05 in the first 10 years and 0.08 thereafter.

　　(ii) 0.08 δ=

　　Calculate the benefit reserve at time 10 for this insurance.

　　(A) 0.144

　　(B) 0.155

　　(C) 0.166

　　(D) 0.177

　　(E) 0.188

　　Exam M: Fall 2005 -37- GO ON TO NEXT PAGE

　　37. For a 10-payment, 20-year term insurance of 100,000 on Pat:

　　(i) Death benefits are payable at the moment of death.

　　(ii) Contract premiums of 1600 are payable annually at the beginning of each year for 10

　　years.

　　(iii) i = 0.05

　　(iv) L is the loss random variable at the time of issue.

　　Calculate the minimum value of L as a function of the time of death of Pat.

　　(A) ? 21,000

　　(B) ? 17,000

　　(C) ? 13,000

　　(D) ? 12,400

　　(E) ? 12,000

　　Exam M: Fall 2005 -38- GO ON TO NEXT PAGE
　　高顿网校之谚语相赠：尽管责任有时使人厌烦，但不履行责任，只能是懦夫，不折不扣的废物。——刘易斯

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