State what is meant by corporate governance. [2]

(ii) Describe the items that should be included in a corporate governance code.

[5]

A social media company which is privately owned is planning an Initial Public

Offering (IPO) and it is considering how to structure bonus payments for senior

employees.

The Remuneration Committee is considering the following proposals to base bonuses

on:

(a) How the share price performs.

(b) How many new users they attract each year.

(c) How the site is rated by its users.

(d) The rate at which the earnings per share grows each year.

(iii) Comment on each of these proposals. [8]

(iv) Suggest the principles which should form the basis of a senior management

bonus scheme. [4]

An actuary is modelling a set of data which consists of 100 consecutive observations,

y1, y2, ... , y100. The data has the following statistics:

y =

1

100 yi

i = 1

100

? = A = 10.5

yi ( ) - y

2

i = 1

100

? = B = 290

( ) yi - 1- y yi ( ) - y

i = 2

100

? = C = 60

( ) yi - 2 - y yi ( ) - y

i = 3

100

? = D = - 240

(i) Calculate the values of the sample auto-correlations r1 and r2. [3]

(ii) Calculate the first two sample partial auto-correlation values

CT6 S2017-6

9

An actuary is modelling a set of data which consists of 100 consecutive observations,

y1, y2, ... , y100. The data has the following statistics:

100

1

2 100

1

100

1

2

100

2

3

1 10.5

100

290

60

240

i

i

i

i

i i

i

i i

i

y yA

yy B

y yy y C

y yy y D

(i) Calculate the values of the sample auto-correlations r1 and r2. [3]

(ii) Calculate the first two sample partial auto- ??? ??? [2]

The actuary is considering two different models for this data:

Model X: t 0 11 t t y a ay

Model Y: t 0 11 2 2 t tt y b by by

where t is a standard white-noise process, with variance ?2

.

(iii) Estimate the parameters (including ?2

) for both Models X and Y, using the

method of moments. [10]

(iv) Explain whether each of Models X and Y satisfy the Markov property

Man Life is an insurance company which only sells life insurance to males. It has recently bought another smaller company called Mixed Life which sells business to both males and females. The company is reviewing the premium rates it charges for life insurance. Man Life has records of the number of policies in force at their year end, which is 30 September, recorded by age last birthday. Mixed Life has records of the number of policies in force on 31 December each year recorded by age last birthday for males and age nearest birthday for females. These are the data for the most recent years. Man Life Age last Number of policies Number of policies Number of policies birthday 30 Sept. 2015 30 Sept. 2016 30 Sept. 2017 49 4,789 4,296 4,367 50 4,953 5,009 4,809 51 5,300 5,186 5,902 Mixed Life Males Age last Number of policies Number of policies Number of policies birthday 31 Dec. 2015 31 Dec. 2016 31 Dec. 2017 49 1,832 1,650 1,698 50 1,800 1,750 1,550 51 1,966 1,756 1,569 Mixed Life Females Age nearest Number of policies Number of policies Number of policies birthday 31 Dec. 2015 31 Dec. 2016 31 Dec. 2017 49 1,602 1,568 1,639 50 1,506 1,497 1,508 51 1,610 1,587 1,411 (i) Calculate the central exposed to risk of the combined portfolio for males aged 50 last birthday for the calendar year 2016, stating each assumption you make at the point where you make it. [5] (Hi) Calculate the central exposed to risk of the combined male and female portfolio for persons aged 50 last birthday for the calendar year 2016, stating each assumption you make at the point where you make it. [3]