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# ct010t07 - UNSW ACTL1001 Actuarial Studies and Commerce...

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UNSW ACTL1001 Actuarial Studies and Commerce Tutorial Exercises 7 Exercise 1 You have a choice of investing \$ 10,000 in one of two potential investments. You must invest in one or the other. The pay-oﬀs from the investments are as follows Outcome Probability Investment A Investment B Good 21 100 6,250 18,750 Middle 74 100 12,500 12,500 Bad 5 100 18,750 6,250 1. Determine the expected value and the standard deviations of the pay-oﬀs from the two investments, 2. Determine the expected utility from the two investments assuming v ( w ) = w - 0 . 000005 w 2 , 3. Which investment would you prefer? Give reasons for your answer. Exercise 2 Assume that you face a loss of \$ 10,000 in damage to your car in the event of a car accident. The probability of a car accident is 0.1 and that the premium for the loss is 5% of the sum insured. Assume you have an initial wealth of \$ 20,000 and that you have a utility function of the form v ( w ) = w - 0 . 000005 w 2 1. Determine your expected utility if you do not purchase insurance, and

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ct010t07 - UNSW ACTL1001 Actuarial Studies and Commerce...

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