Correct solutions are all I need

1.A large defined benefit pension scheme is undergoing a formal actuarial funding

valuation. The trustees have just received a valuation report from the actuary to the

scheme. The report complies with UK professional standards.

(i) Outline the professional requirements that would have applied in the

production of the report. [3]

The scheme has recently closed to new entrants. The sponsor is also considering

ceasing accrual in the scheme.

(ii) Explain how each of these two events might impact the Standard Contribution

Rate and Actuarial Liability. [7]

As part of the report the life expectancy on the valuation basis is shown for members

of the scheme at age 65. This has reduced since the last valuation, whilst the life

expectancy of the general population has increased.

(iii) Suggest reasons why this might have happened. [3]

During the valuation process the sponsor announces that its profits for this year are

expected to be significantly lower than in previous years.

(iv) Discuss how the trustees might react to this announcement

2. An investment bank in the Eurozone has been asked to construct a global corporate

bond index.

(i) Describe a suitable methodology for the construction of the index. [4]

(ii) Discuss some of the specific issues that would need to be considered and

addressed in constructing the index. [6]

(iii) List the possible uses of the corporate bond index

3.

The following diagram shows the transitions under a Healthy-Sick-Dead multiple state model under which: transition rates are dependent on time, f. . transitions out of the Sick state are dependent on the duration, C,, a person has been in the Sick state as well as on time. Healthy Sick p(t, C) H(D) Dead (i) Show from first principles, that if po(x,/) is the probability of being in state / at time / conditional on being in state / at time x, that PHH (x.1) = PHH (x,t)(-a(1)-p(t))+ PHS(x,1)p(t.C,) [5] (ii) Determine the probability that a life is in the Healthy state throughout the period 0 to f if the life is in the Healthy state at time 0. [2] (iii) Describe how integrated Kolmogorov equations can be constructed by conditioning on the first or the last jump, illustrating your answer with a diagram. [3] (iv) Explain the difference in approach between deriving forward and backward integrated Kolmogorov equations. [1] An actuarial student suggests the following integrated Kolmogorov equation for this model: - f(p(u w-s+u)+u(uwe-s+u))du Pr[X, = HWX, = S, C, = w] = [ v(y.w-s+y) PHH (y.1) dy (v) Identify TWO errors in this equation. [2]