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# old6ans - 52 The price of a stock is to be estimated using...

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Unformatted text preview: 52. The price of a stock is to be estimated using simulation. It is known that: (i) The time~t stock price, Sr, follows the lognormal distribution: g, s - 5 " 1%?) ~ JV((or—‘/20'2)t,0'2t) :5 L. 5 (1:) ,0 “[115, {a nger'é] 0 (at - 213 ) f 4 o'Ji-‘e .. ... . e 3 (n) so: 50, a: 0.15, and 0' = 0.30. J‘C'l') - '3» . The following are three uniform (0, 1) random numbers . .. ' i ( 3 a. 0.9830 0.0384 0.7794 2- .» M u. . 3’: 20'2 ”In?" 0")“ Use each of these three numbers to simulate a time~2 stock price. Calculate the mean of the three simulated prices. Sz= S; e (A) Less than 75 (B) At least 75, but less than 85 .2 5 a. @' At least 85, but less than 95 2. I 1 (5". 6 3 .. ms 29. I I (D) At least 95, but less than 115 O . ’W 3):. {2- (E) At least 115 125 (.IS-QEY)(2)+.3E% 8. Total losses for a group of insured motorcyclists are simulated using the aggregate loss model and the. inversion method. The number of claims has a Poisson distribution with P. = 4. The amount of each claim has an exponential ciistribution with mean 1000. The number of claims is Simuiatxsd using '11 = 013 . The claim amounts. are. giniulated using H} = 0.023, H2 = 0,95 and :43 = 0.10 111 that order, as needed. -4 (1,)“ r“ ”a n . Deremﬁne the total losses. 17mm»: ( rm ﬂ" 1].. ‘F V“ (A) 0 0 0.0183 (3.0le (B) 51 i 0.0933 0.0‘HS é.- use ‘3 “I 0.23? ' ' (C) 2996 2 9' ' I 304? (E‘ 3152 j u. = 0.1;: ’5 l4 ' 2- (Exam 4/C, Fall 2005) . ’x/looe @‘Poﬂ. ' U- : ch) :- l-e_ " x ’ﬂ/IOO‘ — I- :5.- I-o‘B—a = “((‘u\ :5 a .- U u. .35... 0:; .5“: M O. a," Z‘HS‘D3 WW 304'). 01v % ...
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