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Tut4Sol

# Tut4Sol - ACTSC 232 SPRING 2010 TUTORIAL 4 First(given Name...

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Unformatted text preview: ACTSC 232 - SPRING 2010 - TUTORIAL 4 First (given) Name: SOLUTSO NS Last (family) Name: ID #: UserID: 1. Describe in words the insurances with the present values given (try Without consulting your notesl). You should specify how much beneﬁt is paid under every possible circumstance. V 2000007?» Tm< 15 20,000 Fm \Mmszocieb w, Qua-HA MAMA ( ) 21 = 15’ — ~ - . r - . . 100000 , Tx>15 l5 39M»; , or 10,000 Pods cm svwwcd +o 15. (b) 2 __ 1000mm“, ngg 10/000 Fara amt +lxxe.e/m.d 5? +qu ﬂew 2’ 0, Ktzm 0f @QHAIF Wavexio jaws 2. Express E[Z1] and E[Z2] above using ’A’ type actuarial functions. . \ . 1 EEZJ :QoloooZ;_m + iolom Arm BUZZ] : (soooAlwm 0F 2,9,OOOAXt31 _. [01000,Ax;%l or lOOOO -/Tx: ﬂ + [O ODOAXICEW 3 Given um”: 11 for all t > 0, derive expressions (and simplify as far as possible) for “Judi“ the following functions, assuming a constant force of interesétfjC M Noki e] x I C vat _ W 'S‘E e’ﬂf _ H e/ + * 1 €— (3)1491 :0 a ﬂd‘t - [/KN/Z+S If " M+S -1 b h _gé€— '_ / ‘ ' .; v-(M g)( n — _ €‘W+\$)11l (b) Amzﬁ - 0/6. Qﬂ+Md{ -7 [»/M\—%] ’ /{/L+5:{‘ (c) Amnl __ 68“ C—MK : C— (yr/1+9 a (d) The variance of the PVRV for an n—year term insurance with sum insured S issuedto (51:) \ L ‘3 (As W ‘ AQW) , »(/A+S)u L, : 32(M/jlgﬂ «0141:29ka (ﬁg (l ‘ 6, >> ) 4. Z3 is the PV of an n-year term continuous insurance beneﬁt, issued to (ac) Z4 is the PV of a continuous whole life insurance beneﬁt, issued to the same life. What is the covariance of Z3 and Z4? Express in actuarial functions, simplied as far as possible. so 3324-: (vi? 1t~1x4w EEZ5 Zr]: Ax m +tW5 00V (£31,230: EEZB 2&1] @251 EEZHJ ‘“ Ml‘m IMHW 2X} X . ...
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