1 (i) Describe how a classification based on the nature of the state and time spaces of stochastic processes leads to a four-way categorisation. [2]

(ii) List FOUR stochastic processes, one for each of the four categories in your

answer to part (i). [2]

2 (i) Define a Markov Chain. [2]

(ii) Describe the difference between a time-homogeneous and a time inhomogeneous Markov Chain, giving an example of each.

3 (i) List the uses of investment indices. [3]

(ii) Describe the main components of the FTSE UK Index Series of indices. [8]

The trustees of a self-administered UK pension fund are considering the choice of an index against which the fund's UK equity performance could be benchmarked.

(iii) Propose, with reasons, indices that might be adopted for this purpose.

4 (i) Outline the benefits that can be provided to members of a defined contribution pension scheme. [4]

(ii) Compare the financial risks of a defined contribution pension scheme with those of a defined benefit pension scheme for:

(a) a member and

(b) an employer.

5 A company sponsoring a non-contributory defined benefit pension scheme has decided to amend the scheme to provide benefits on a defined contribution basis for future service.

The benefits payable for service prior to the date of amendment are set out below:

Normal Pension Age (NPA) 60

Accrual rate 1/60ths of Final Pensionable Salary for

each year of pensionable service

Commutation at NPA Maximum of 20% of member's pension with each 1 p.a. of pension

providing 12 of cash

Final Pensionable Salary Average of basic pay at 1 April for the

three year period prior to leaving

Pension increases in payment 3% p.a.

Spouse's pension on death before NPA 1/3rd of basic pay on 1 April prior to

death Lump sum on death before NPA 5 times basic pay on 1 April prior to

deathSpouse's pension on death after NPA 50% of member's pension at date of

death

An extract of the minutes of the company board meeting where the decision was taken

is as follows:

"The company's objective is to reduce the financial risks associated with the current pension scheme, and to offer a replacement scheme having the same expected long

term cost for future service."

(iii) Calculate the rate (as a percentage of basic pay) at which the company willneed to contribute to the defined contribution scheme in order to try to achieve this objective. State the assumptions you have made and show your workings.

[8]

(iv) Discuss why the cost of the new pension benefits might differ from the cost of

the current scheme, assuming that the company pays contributions at the rate

calculated in part (iii).