INTRODUCTION TO RISK MANAGEMENT ASSIGNMENT
1. Assume that United Delivery Service (UDP), a mail service company, has distribution centers all along the East coast. UDP uses a fleet of 900 delivery trucks in its operations dispersed among the various distribution centers. From past information the Chief Risk Officer for UDP has constructed the following probability distribution for the number of losses per truck per month.
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# of losses per truck per month
|
Probability
|
|
0
|
0.30
|
|
1
|
0.25
|
|
2
|
0.20
|
|
3
|
0.16
|
|
4
|
0.09
|
a. Calculate expected value of frequency per truck per month.
b. Calculated the variance.
2. Now assume that when truck losses do occur, they are non-random and always equal to $800.
a. Calculate the expected loss per truck per month?
b. Calculate the expected loss for ALL trucks per month.
c. Calculate the expected loss for ALL trucks for the year.
3. UDP has one major competitor on the East Coast, Speedy Delivery (SD). SD has similar operations and services as does UDP. However SD has a smaller fleet of trucks, with 500 trucks dispersed throughout the region. From past information SD has collected the following data for the number of losses per truck per month.
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# of losses per truck per month
|
# of trucks having these losses
|
|
0
|
200
|
|
1
|
150
|
|
2
|
100
|
|
3
|
???
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|
4
|
10
|
a. As a new hire in SD's risk management department, you are asked to derive the probability distribution for frequency based on the information provided above.
b. Now you are an insurance underwriter, looking at submissions from both UDP and SD. You would like to know which company faces the most risk? Show/Explain how you came to this answer.
4. From past information, SD has constructed the following distribution related to dollar amount of losses when accidents do occur.
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$ amount of losses
|
Probability of dollar loss
|
|
100
|
0.60
|
|
600
|
0.30
|
|
1200
|
0.07
|
|
2000
|
0.03
|
a. Calculate the expected value of severity for SD.
b. Calculate the expected loss per truck per month.
5. Miranda's Muffins sells muffins in Philadelphia. They have been baking and selling muffins in the city for 5 years. While they generally produce just enough to sell for the week, there are occasions when they bake more than they can sell, sometimes way more than they can sell, which forces them to throw the product out. Here is the data that Miranda's Muffins has collected over the last 5 years in weeks:
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Muffins Wasted
|
Number of Weeks
|
|
0
|
140
|
|
25
|
60
|
|
50
|
40
|
|
100
|
15
|
|
200
|
5
|
a. What is the probability of each loss (Create a probability distribution)?
b. Calculate the variance of the muffin loss.
c. Calculate the coefficient of variance for the muffin loss.
6. Amazon has three packages (Package A, Package B, and Package C) that is to be shipped to Bill's address. Package A is worth $50, Package B is worth $150, and Package C is worth $250. All three packages have a 80% chance of arriving and a 20% chance of being lost in transit. Set up a probability distribution with the appropriate probabilities for each possible outcome. What is the expected loss (P*)? How much risk does Amazon face in this delivery purchase. (i.e. -what is the coefficient of variation)?