Actuaries Cmp Upgrade 2009-10

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CT4: CMP Upgrade 2009/10

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Subject CT4
CMP Upgrade 2009/10
CMP Upgrade This CMP Upgrade lists all significant changes to the Core Reading and the ActEd material since last year so that you can manually amend your 2009 study material to make it suitable for study for the 2010 exams. It includes replacement pages and additional pages where appropriate. Alternatively, you can buy a full replacement set of up-to-date Course Notes at a significantly reduced price if you have previously bought the full price Course Notes in this subject. Please see our 2010 Student Brochure for more details.

This CMP Upgrade contains: • • All changes to the Syllabus objectives and Core Reading. Changes to the ActEd Course Notes, Series X Assignments and Question and Answer Bank that will make them suitable for study for the 2010 exams.

The Actuarial Education Company

© IFE: 2010 Examinations

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CT4: CMP Upgrade 2009/10

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1.1

Changes to the Syllabus objectives and Core Reading
Syllabus objectives
Syllabus objective (ix)8 has been changed and now reads: 8. Develop census formulae given age at birthday where the age may be classified as next, last, or nearest relative to the birthday as appropriate. The deaths and census data may use different definitions of age.

1.2

Core Reading
Chapter 2
Page 8 A new paragraph has been added. A replacement page is provided at the end of this document.

Chapter 3
Page 7
The following Core Reading has been added before the proof on Page 7. Students should understand this proof, but they will not be expected to reproduce it in the examination.

Chapter 5
Page 29
The following Core Reading has been added before the proof on Page 29. Students should understand this proof, but they will not be expected to reproduce it in the examination.

Chapter 7
A section entitled “Simple parametric survival models” has been added. Replacement pages are provided at the end of this document.

© IFE: 2010 Examinations

The Actuarial Education Company

CT4: CMP Upgrade 2009/10

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Chapter 8
The Core Reading in Section 3 has been rewritten and a new section of Core Reading has been added to the end of the chapter. Replacement pages are provided at the end of this document.

Chapter 10
Page 14 The sentence in the first paragraph that begins “And, as we have seen …” has been deleted from the Core Reading.

Chapter 11
The Core Reading in Sections 7 and 8 has been deleted, ie calendar year and policy year rate intervals have been removed from the course.

The Actuarial Education Company

© IFE: 2010 Examinations

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CT4: CMP Upgrade 2009/10

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Changes to the ActEd Course Notes
Chapter 5
Page 44 A note on the second-order condition for maxima has been added. Replacement pages are provided at the end of this document.

Chapter 7
Page 10 A section on life tables has been added. Replacement pages are provided at the end of this document.

Chapter 10
This chapter has been moved from Part 3 to Part 4 of the course.

Chapter 11
Section 9 has been deleted (because it was about calendar year and policy year rate intervals, and these have been removed from the course).

© IFE: 2010 Examinations

The Actuarial Education Company

CT4: CMP Upgrade 2009/10

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Changes to the Q&A Bank
Part 2
The following question has been added. Question Consider the following time-inhomogeneous Markov jump process with transition rates as shown below:

0.1t 0.1t

2
0.2t

1
0.05t

0.2t

4
0.5t

3

(i) (ii)

Write down the generator matrix at time t .

[2]

Write down the Kolmogorov backward differential equations for P33 ( s, t ) and P ( s, t ) . 13 [3]

(iii)

Using the technique of separation of variables, or otherwise, show that the solution of the differential equation for P33 ( s, t ) is: P33 ( s, t ) = e -0.25 t 2 - s 2

(

)

[4]

(iv)

Show that the probability that the process visits neither...
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