A house holder is currently considering insuring the cont - PowerPoint Presentation

A  house holder is currently considering insuring the cont
A  house holder is currently considering insuring the cont

A house holder is currently considering insuring the cont - Description


He estimated the contents of his house would cost him 20000 to replace Local crime statistics indicates that there is a probability of 003 that his house will be broken into in the coming year ID: 596058 Download Presentation

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100 000 150 house 000 100 house 150 8500 year theft company 347 policy 177 contents insuring insurance loss

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Slide1
Slide2

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

Shom More....