Actuarial Mathematics 2: Assignment 1
\nQuestion 1:
\n(a) Prove that if \u00b5 is constant then
\n +
\n for all
\n =
\n +
\n , \u2265 0
\n(b) For a Whole Life Policy with death benefit of $5000, benefit
\npayable at the end of year of death, determine 1 given<\/p>\n
\u00b5 = 0. 07 and = 0. 07.
\n(c) Consider the following information for a given policy :
\na. \u03b4 = 0. 03
\nb. Level premium = $3500
\nc. No expenses.
\nd. \u00b5 = 0. 0007
\ne. Benefit payment = $150, 000
\n(i) Using Thiele\u2019s Differential Equation, solve analytically (using
\ncalculus) for the policy value .
\n(ii) Find the unique solution to this differential equation clearly
\nshowing why this is the case.
\n(iii) Describe the what happens to the policy value as \u2192 \u221e.
\n(d) Consider the following policy basis for a 20 year term life policy
\nwith:
\nSurvival model: De Moivre\u2019s Law \u03c9 = 105
\nInterest: = 0. 06
\nExpenses: No expenses
\nSum Insured: $60,000
\nBy using Microsoft Excel or otherwise, determine 10 using the
\nnumerical approximation (Euler\u2019s Method) for the solution to
\nThiele\u2019s Differential Equation. Assume a time step of \u210e = 0. 05.
\nTotal: 20 marks
\nQuestion 2:
\nConsider the following joint density function for (2) lives (x) and (y):
\n ( , ) = ( , ,
\n2
\n+
\n2
\n) 0 < < 3 0 < < 2
\n(a) Calculate .<\/p>\n
(b) Calculate .<\/p>\n
(c) For a whole life policy of a joint status (following the mortality
\nmodel above) with sum insured of $250,000, benefit payable
\nimmediately upon death, determine the net single premium.
\nTotal: 15 marks<\/p>\n","protected":false},"excerpt":{"rendered":"
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