Table 1: Answer Key: Place all your answers here for consideration
Q# Answer
1
a
2
a
3
a
4
d
5
d
6
d
7
a
Michigan State University
Department of Mathematics
STT 456 Spring 13
TEST 3
Name (Print): Solutions
Name (Sign):
Case 1: A double-decrement lapse mo
Suggested solutions to DHW textbook exercises
Exercise 8.2
(a) Writing out the Kolmogorovs forward equations for tp00 , we have
30
d 00
01 10
02
02
01
00
tp30 = tp30 30+t tp30 30+t + 30+t + 30+t
dt
.
Notice that we need values for tp01 so that the corresp
Suggested solutions to DHW textbook exercises
Exercise 8.1
Note the ip-op in the s according to the Errata.
(a) Since you cannot return to state 0 once you leave the state, we must have:
t
5 t
01 s + 02 s ds = e10
30+
30+
00
00
tp30 = tp30 = exp
Bc30
t
Suggested solutions to DHW textbook exercises
Exercise 7.14
In the subsequent development of the formulas, we shall denote by P the applicable single
benet premium to be paid at time of policy issue.
(a) Starting with 0 V = 0, the recurrence relation betw
Suggested solutions to DHW textbook exercises
Exercise 7.13
(a) In general, with no expenses, the Thieles dierential equation can be expressed as
d
t V = t t V + P (St t V )[x]+t .
dt
For this problem, premiums are level payable continuously at the rate P
Michigan State University
Department of Mathematics
STT 456 Spring 13
TEST 1
Name (Print):
Name (Sign):
Case 1: A whole life insurance with reduced early sum insured is issued to a
life age 50. The sum insured payable at the end of the year of death in th
Michigan State University
Department of Mathematics
STT 456 Spring 13
TEST 2
Name (Print):
Name (Sign):
Basic Information: As promised, the Forward Euler approximation for
the Kolmogorov equations are
n
ij
t+h px
=
ij
t px
n
ik kj
t px x+t
+h
jk t .
x+
ij
Michigan State University
Department of Mathematics
STT 456 Spring 13
TEST 2
Name (Print):
Name (Sign):
All Answers Must Be Entered Into This Answer Key
Question Number
1
2
3
4
5
6
7
Answer
c
b
b
c
a
d
b
Basic Information: As promised, the Forward Euler a
Michigan State University
Department of Mathematics
STT 456 Spring 14
TEST 1
Name (Print):
Name (Sign):
All Answers Must Be Entered Into This Answer Key
Question Number
1
2
3
4
5
6
7
Answer
d
e
a
b
b
b
a
Case 1: Smith, a 40 year old man, takes out a 30yea
Table 1: Answer Key: Place all your answers here for consideration
Q# Answer
1
f
2
a
3
a
4
b
5
c
6
a
7
a
Michigan State University
Department of Mathematics
STT 456 Spring 13
TEST 4
Name (Print): Solutions
Name (Sign):
Case 1: A ve year policy with annua
Suggested solutions to DHW textbook exercises
Exercise 7.11
(a) Let G be the required annual gross premium. The APV of future premiums is
APV(FP0 ) = G a[40]: 10 ,
the APV of future benets is
APV(FB0 ) = 20000 A[40]: 10 1000010 E[40] ,
and the APV of futu