This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 (.ISQEY)(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) : le_
" x
’ﬂ/IOO‘ — I :5. Io‘B—a = “((‘u\
:5 a . U u. .35...
0:; .5“: M
O. a," Z‘HS‘D3
WW
304'). 01v
% ...
View
Full Document
 Winter '08
 Staff

Click to edit the document details