Actuarial Mathematics 2: Assignment 1
\nQuestion Assignment 1:
\n(a) Show that if \u00b5 is fixed then
\n +
\n for all
\n =
\n +
\n , \u2265 zero
\n(b) For a Entire Life Coverage with loss of life advantage of $5000, profit
\npayable on the finish of 12 months of loss of life, decide 1 given<\/p>\n
\u00b5 = zero. 07 and = zero. 07.
\n(c) Take into account the next info for a given coverage :
\na. \u03b4 = zero. 03
\nb. Stage premium = $3500
\nc. No bills.
\nd. \u00b5 = zero. 0007
\ne. Profit fee = $150, 000
\n(i) Utilizing Thiele\u2019s Differential Equation, resolve analytically (utilizing
\ncalculus) for the coverage worth .
\n(ii) Discover the distinctive answer to this differential equation clearly
\nexhibiting why that is the case.
\n(iii) Describe the what occurs to the coverage worth as \u2192 \u221e.
\n(d) Take into account the next coverage foundation for a 20 12 months time period life coverage
\nwith:
\nSurvival mannequin: De Moivre\u2019s Legislation \u03c9 = 105
\nCuriosity: = zero. 06
\nBills: No bills
\nSum Insured: $60,000
\nThrough the use of Microsoft Excel or in any other case, decide 10 utilizing the
\nnumerical approximation (Euler\u2019s Methodology) for the answer to
\nThiele\u2019s Differential Equation. Assume a time step of \u210e = zero. 05.
\nComplete: 20 marks
\nQuestion Assignment 2:
\nTake into account the next joint density perform for (2) lives (x) and (y):
\n ( , ) = ( , ,
\n2
\n+
\n2
\n) zero < < three zero < < 2
\n(a) Calculate .<\/p>\n
(b) Calculate .<\/p>\n
(c) For an entire life coverage of a joint standing (following the mortality
\nmannequin above) with sum insured of $250,000, profit payable
\ninstantly upon loss of life, decide the online single premium.
\nComplete: 15 marks<\/p>\n","protected":false},"excerpt":{"rendered":"
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