Presentation on theme: "A house holder is currently considering insuring the cont"— Presentation transcript
Slide1Slide2
A
house holder is currently considering insuring the contents of his house against theft for one year.
He
estimated the contents of his house would cost him £20,000 to replace
.
Local
crime statistics indicates that there is a probability of 0.03 that his house will be broken into
in
the coming year.
In
that event his losses will be 10%, 20% or 40% of the contents with probabilities 0.5, 0.35
and
0.15 respectively.
An
insurance policy from Company A costs £150 a year but guarantees to replace any loss
due
to the theft.
An
insurance policy from Company B will be cheaper at £100 a year but the householder has
t
o
pay the first £x of any loss himself.
An
insurance policy from Company C is even more cheaper at £75 a year but only replaces a
fraction
of any loss (y%) suffered.
Assume that there can be at most one theft a year.
Draw
a decision
tree
and give
your advice to the house holder if x=50, y=40 and his objective is to maximize the
expected
monitory value(EMV)?Slide3
FINAL DECISION
WHICH COMPANY?
IF NOT INSURED
IF INSURED
150 £
100 £
B
C
A
75 £
0.5
0.35
0.15
0.97
0.03
0.97
0.97
0.03
0.03
0.97
0.03
0.5
0.35
0.15
0.5
0.35
0.15
0.5
0.35
0.15
1
2
3
4
5
6
7
8
9
10
11
12
13
14
16
17
18
15
19
20
21
22
23
24
25
26
A
B
C
NISlide4
T - NODE
CALCULATION 0F PROFIT
PROFIT
PROB
T
-
EMV
11
COST OF INSURING =
(-150)
0.97
(-145.5)
12
2,000 – 150 =1,850
0.5
92513
4,000 – 150 =3,850
0.35
1,347.514
8,000 – 150 =
7,850
0.15
1,177.515
COST OF INSURING =
(-100)0.97
(-97)
162,000 – 100 – 50 =
1,8500.5
92517
4,000 – 100 – 50 =
3,850
0.351,347.5
18
8,000 – 100 – 50 =7,850
0.15
1,177.5
19
COST OF INSURING =(-75)
0.97(-72.75)
20
2,000 – [2,000 x (40/100)] – 75 =1,125
0.5
562.521
4,000 – [4,000 x (40/100)] – 75 =
2,3250.35
813.75
228,000 – [8,000 x (40/100)] – 75 =
4,725
0.15
708.75
23NOT INSURED & NO THEFT =0
0.970
2420,000 x (10/100) =
(-2,000)0.5
(-1,000)25
20,000 x (20/100) =(-4,000)0.35
(-1,400)
26
20,000 x (40/100) =(-8,000)
0.15(-1,200)
A
B
C
NISlide5
C - NODE
CALCULATION
C - EMV
7
925 + 1,347.5 + 1,177.5 =
3,450
8
925 + 1,347.5 + 1,177.5 =
3,450
9
562.5 + 813.75 + 708.75 =
2,085
10
(-1,000) + (-1,400) + (-1,200) =
(-3,600)3
(3,450 x .03) + (-145.5) =
(-42)4
(3,450 x .03) + (-97) =
6.55
(2,085 x .03) + (-72.75) =
(-10.2)
6
(3,600 x .03) + 0 =(-108)
The best choice that the house holder can make is to insure the contents of the household with the
company B, which gives him the highest EMV of 6.5. In such case if there happens to be a theft at his house he will be safe even though he has to bear an amount of £50 on his own. This insurance policy comes with a premium
of £100.
A
B
C
NI
