Address these questions appropriately explaining each step of your working.
10 An investment project has been evaluated using Monte Carlo simulation. After running the simulation 2.5 million times, the results have stabilised and the expected net present value is positive and averages $1 million, with a range of outcomes varying from minus $200,000 to plus $1.8 million. Which of the following statements best interprets these results? A The project satisfies the net present value criterion. B The project should definitely proceed. C This is a low risk project. D The model should be run another 2.5 million times in order to be certain. [2] 11 Joan is an actuarial consultant who has operated as a sole trader for several years. She has decided to bring Frank, a colleague, into the business. Describe the advantages to Joan of a traditional partnership over a limited company for the business arrangement with Frank. [5] 12 Describe the usefulness of bank overdrafts in managing a company's working capital requirements. [5]Collecting further information from the insured takes an average of 5 days to complete, and immediate settlement takes an average of 2 days before the settlement process is complete (state C). It is suggested that a time-homogeneous Markov process with states A, L, I, S and C could be used to model the progress of claims through the settlement system with the ultimate aim of reducing the average time to settle a claim. (i) Calculate the generator matrix, (1;;i, j = 4, L, I, S, C}, of such a model. [ (ii) Calculate the proportion of claims that eventually require more details from the insured. [2] (iii) Using a forward differential equation, derive an expression for the probability that a claim is yet to be logged and classified by a claims administrator at time /. [4] (iv) Write down the backward integral equation for the transition probability PA, (t), and hence show that: PAI (1) = 0.05 [ e-0.50w PLI (t - w) dw + 0.25e-0.20r [' e-0.30w [3] (v) Using the expression in (iv), show that: PAI (1) =- -0.101 47 -0.20r 197 -0.50r 60 [6] 80 240 (vi) Calculate the probability that a claim is still awaiting information from the insured after 10 days. [1] (vii) Describe briefly how you could verify that this time homogeneous rather than an alternative time inhomogeneous model was a suitable model of the claims' settlement process. [2] [Total 20]Claims on an insurer's travel insurance policies arriving in the claims department (state A) wait for an average of two days before being logged and classified by a claims administrator as requiring: investigation by a loss adjuster (state L), more details from the insured (state D), no further information is required and the claim should be settled immediately (state S). Only one new claim in ten is classified as requiring investigation by a loss adjuster, and five in ten require further information from the insured. If needed, investigation by a loss adjuster takes an average of 10 days, after which 30% of cases require further information from the insured and 70% are sent for immediate settlement
