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(b)        Describe your distribution of the total weekly claims cost.

(c)        How much money should NRCV have available in liquid assets to cover the weekly amount

(total weekly claims cost) for small passenger car claims?  Discuss, and make a recommendation to NRCV.  Give reason(s) for your recommendation.

3.         On the basis of your simulation of the total weekly claims cost, estimate the

(a)        probability that \$35,000 will be sufficient to keep in liquid assets to cover weekly claims.

You must explain how you obtained this estimate.

(b)        95th percentile of total weekly claims cost.

You must explain how you obtained this estimate.

4.         “Naïve analysis

An estimate of the mean total weekly claims cost (TWCC) can be obtained by combining the mean values of the random variables which are described in the “Model – Assumptions”.

(This estimate is obtained without performing a simulation like you did in the “original analysis” above.)

(a)                Naïve analysis: show how these mean values can be combined to produce an estimate of the

mean total weekly claims cost and calculate this estimate.

(b)               In comparison with the simulation (“original analysis”) above, briefly discuss what you consider to be deficient in this naïve analysis of the given model.

5.         Discussion

Consider the original (not the naïve) analysis for deciding how much money to keep in liquid assets to

cover the weekly amount (total weekly claims cost) for small passenger car claims.  Discuss any further

points which you think should be made about the original analysis, for example, any features or

limitations or recommendations.  Your discussion must relate to the current NRCV problem.

##### SECTION II                                                                                                                [34 marks]

Management of a large shopping centre are offering to their tenant shopkeepers an insurance policy to protect against damage to premises.  Shopkeepers are being asked to choose from amongst the following three policy options.

·         A full policy has a premium of \$200,000 per annum and would cover 100% of any loss in excess of \$100,000, ie, a \$100,000 ‘excess’ to be paid by the policyholder (shopkeeper).

·         A partial policy has a premium of \$120,000 per annum and would cover 100% of any loss in excess of \$300,000, ie, a \$300,000 ‘excess’ to be paid by the policyholder (shopkeeper).

·         Self-insurance involves no premium, but 100% of any loss is to be borne by the shopkeeper.

[Management may offer a discount on the premiums.  The same percentage discount would be applied to both the full and the partial policies.  So, you need to set up your input table to allow for this possibility.]

The following probability distribution of damage for these shops has been estimated.

 Damage (\$m) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 Probability 0.4 0.3 0.13 0.06 0.05 0.03 0.02 0.01

Decision tree analysis

(a)                Construct an input table for your analysis.

(i)                 Include excess, premium, percentage rate of discount and discounted premium

amount.  Show the formula for calculating discounted premium.

(ii)        Also include the ‘above premium’ cost (the cost, but disregarding the premium)

to the shopkeeper under each policy option/damage amount combination.

(b)               (i)         Using PrecisionTree, construct a decision tree for this problem.

Assume 0% discount on premiums at this stage of the analysis.

(ii)               On the basis of this decision tree analysis, which decision should a shopkeeper make?  Give reason(s) for your answer.

(iii)             PrecisionTree calculates the Expected Monetary Value for the optimum decision.  Show how this calculation was done.

(c)                (i)         Tabulate the total cost, (including the premium) that the shopkeeper would incur

under each policy option/damage amount combination.

(ii)        Calculate the expected value of perfect information (EVPI).  Show your working.

(iii)       State the value of EVPI and interpret it.

(d)               The shopkeepers may be offered a discount on the premium amount.  (The same percentage discount would be applied to both the full and the partial policies.)

(i)                 Perform a sensitivity analysis on the optimal decision, by varying the percentage rate of

discount.  Graphs and tables must be fully and appropriately labelled.

(ii)        Report your findings from the sensitivity analysis.

(e)        Write down any further comments or advice you can offer to the shopkeepers in relation to

the policy options.

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