8 - Catastrophe Modeling. Suppose you just bought a new sports car. Based on his

Question

8 - Catastrophe Modeling. Suppose you just bought a new sports car. Based on historical data of the city you live in, there is a 5% chance that a car gets severely damaged within the first five years of purchase. If your car gets severely damaged, your estimated loss is $50,000 Now you have the option of buying a premium insurance plan that can cover your loss if your car gets severely damaged within the next five years. The insurance plan costs $2,000 total and it covers your loss with 95% probability (i.e., if you severely damage your car within the first five years, with 5% chance, the insurance company doesnt cover your loss). (1) What is your expected loss if you don't get the insurance? What is the standard deviation of the loss (6pts)? (2) What is your expected loss if you get the insurance? What is the standard deviation of the loss (8pts)?

Explanation / Answer

Solution- (a) Let L be the random variable of the loss if insurance isn't bought. Then Expected value of L will be calculated as-

E( L ) = 0 * 0.95 + 50000 * .05

= 2500

now E( L2 ) = 02 * 0.95 + 500002 * .05

= 125000000

SO var(L) = E( L2 ) -[ E( L ) ]2

= 125000000 - 25002

= 118750000

So standard deviation = 1187500000.5

=10897

(b) Let X be the random variable of the loss if insurance is bought. Then Expected value of X will be calculated as-

E( X) = 2000 * 0.95 + ( 50000 *.05 + 2000 ) * .05

= 2125

now E( X2 ) = 20002 * 0.95 + 500002 * .05 * .05 + 20002 * .05

= 10250000

SO var(X) = E( X2 ) -[ E( X ) ]2

= 10250000 - 21252

= 5734375

So standard deviation = 57343750.5

= 2394.66

Answers

TY!

Please rate the solution!

Related Questions

Navigate

• Browse (All)
• Browse 8
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.