Fall 2002 - Course 3 Solutions

Question #23
Answer: C
Time of first claim is T 1 = − 1/ 3log 05 . = 023 .
0.
23
b g . Size of claim = =
Time of second claim is T 2 = 0. 23− 1/ 3log 0. 2 = 0.
77
Time of third claim is T 3 = 077 . − 1/ 3log 01 . = 1.
54
10 1.
7
0.
77
b g . Size of claim = =
1.
54
b g . Size of claim = =
Since initial surplus = 5> first claim, the first claim does not determine c
0 z.
77
4
Test at T 2 : Cumulative assets = 5 + ct dt = 5 + 0 . 054c
Cumulative claims = 1.7 + 5.9 = 7.6
Assets ≥ claims for c ≥ 4815 .
Test at T 3 : Cumulative claims = 1.7 + 5.9 + 34.7 = 42.3
Cumulative assets = 5+ ct dt = 5+
1732 . c
0
z. 154
0
Assets ≥ claims for c ≥ 2154 .
If c < 4815 . , insolvent at T 2 .
If c > 4815 . , solvent throughout.
49 is smallest choice > 48.15.
4
10 5.
9
10 34.
7
Question #24
Answer: C
µ xy = µ x + µ y = 014 .
µ
Ax
= Ay
=
+ = 007 .
= 05833 .
µ δ 007 . + 005 .
µ xy
Axy
=
axy
+ = 0.
14 014 .
1
= = 0 7368 =
µ δ 0 14 + 0 05 019
µ + δ
= 1
. and
. . .
014 . + 0.
05
xy
P
A xy A + A − A
= =
a a
xy
x y xy
xy
b g
2 0. 5833 −0.
7368
=
= 0.
0817
52632 .
xy
= 5.
2632