test1_00 - ACT348F TERM TEST 1 Print your name and student...

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ACT348F - TERM TEST 1 - OCTOBER 11, 2000 Print your name and student number clearly on each page Do all work on this question paper, with work for question 1 on this page (use both sides if necessary), work for question 2 on the next page, etc. All calculations should be done to . at least 6 digit accuracy Answers are expected to have at least 4 digit accuracy. 1. A three-year fully discrete endowment insurance with face amount $1000 is issued at age , B with level annual premium of payable at the start of each year . The mortality U for two years probabilities are , and the annual effective interest rate is ;& ± ; & ± ;& B " B²# " "" % $# 10%. (a) Write out the point-by-point expression for the issue-date loss random variable . P (b) Find the equivalence principle premium. (c) Suppose that . Find . U&³! ! Z +<´Pµ Solution: (a) if P& "!!!@¶U&*!*·!*¶ U O&!±; &"˛% "!!! @ ¶U—"²@¸&)#’·%³¶"·*!*!* U O&" ± ; &"˛% "!!! @ ¶U—"²@¸&(³"·$"¶"·*!*!* U O¹# ±: &"˛# & B # "l B $ # B (b) I´Pµ&´*!*·!*¶Uµ—·#³¸²´)#’·%³¶—"·*!*!*¸Uµ—·#³¸ ²´(³"·$"¶—"·*!*!*¸Uµ—·³¸&)!*·³%¶"·’)")#U&!pU& %)"·$³
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This note was uploaded on 09/27/2009 for the course ACT 348 taught by Professor Broverman during the Fall '04 term at University of Toronto.

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test1_00 - ACT348F TERM TEST 1 Print your name and student...

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