1. Which of the following statements is NOT true of investment trusts?
A They are public companies.
B They can raise both loan and equity capital.
C They are open-ended investment vehicles.
D Their shares are usually quoted.
2
(i) Set out the key risks and uncertainties of defined benefit and defined contribution pension schemes. [6] (ii) Suggest possible ways in which the risks in part (i) could be mitigated. [6] A large company is about to set up a new defined contribution pension scheme. (iii) Set out the key aspects of the defined contribution pension scheme design that need to be considered. [6] The defined contribution pension scheme will provide a guarantee that the investment returns on members* funds before retirement will not fall below 0%. (iv) Outline the design considerations involved in offering the investment guarantee. [3]The price process of a non-dividend paying stock S, satisfies the following stochastic differential equation dS, = us,dr + oS,dW. where W, is a Brownian motion under the real-world probability measure P. Let V(1) be the value at / of a self-financing portfolio, consisting of , stocks and , cash bond. (i) Show that d(e "V (1)) = 0 d(e "s;). [3] (ii) Determine the conditions under which the discounted value e "V () is a martingale. [3]Claims on a portfolio of insurance policies arise as a Poisson process with parameter 2.. Individual claim amounts are taken from a distribution X and we define m; = E(X') for / = 1, 2, .... The insurance company calculates premiums using a premium loading of 0. (i) Define the adjustment coefficient R. [1] (ii) Show that R can be approximated as 20171. by truncating the series expansion of My(1). m2 [3] Now suppose that X follows an exponential distribution with parameter y. (iii) Show that R = [3] (1+0) The insurance company uses a premium loading of 12%, and the mean claim amount is 200. (iv) Calculate R, commenting on the difference with the approximation to R shown in part (ii). [3] The initial surplus is 5,000. (v) Calculate an upper bound for the ultimate probability of ruin. [1] (vi) Suggest two methods by which the insurance company can reduce the probability of ruin. [2]
