6. Suppose you were an actuary for a company that insured oceanfront homes. In t

Question

6. Suppose you were an actuary for a company that insured oceanfront homes. In this specific housing development, the homes are worth about $1,500,000 each. Based on historical data and previous insurance claims, a tropical storm that occurs about 14% of the time causes about 1% of the value of the home in damage. A category 1 hurricane that happens 8% of the time results in about 5% of the home value in damage. For a category 2 hurricane occurring about 5% of the time, 10% of the value of the home will result in damage. A category 3 hurricane takes place about 1% of the time and causes about 20% of the value of the home in damage. A category 4 hurricane turns out about 1% of the time and results in about 70% of the total home value in damage. The total value of the home is virtually wiped out at 100% of the home value for a category 5 hurricane that happens 1 % of the time. Let the random variable X represent the claim amount for a year. Fill in the probability distribution table below. Hint: Remember that hurricanes do not necessarily happen every year, so think about the claim amount and associated probability for that to occur.

X

P(X)

X

P(X)

Explanation / Answer

Here,

Worth of homes = $1,500,000

(a) For 14% homes

Damage = 1%

Amount damage = 1500000 * 1% = $15000

Probability of that occuring = 0.14

(b)

For 8% homes Cartegory I damage

Damage = 5%

Amount damage = 1500000 * 5% = $75000

Probability of that occuring = 0.08

(c)

For 5% homes Cartegory II damage

Damage = 10%

Amount damage = 1500000 * 10% = $150000

Probability of that occuring = 0.05

(d)

For 1% homes Cartegory III damage

Damage = 20%

Amount damage = 1500000 * 20% = $300000

Probability of that occuring = 0.01

(e)

For 1% homes Cartegory IV damage

Damage = 70%

Amount damage = 1500000 * 70% = $1050000

Probability of that occuring = 0.01

(f)

For 1% homes Cartegory IV damage

Damage = 100%

Amount damage = 1500000 * 100% = $150000

Probability of that occuring = 0.01

(g) the probability of no damage from hurricane = 1 - sum of all probabilities = 1 - 0.3 = 0.7

So, the probability distribution

Category Hurricane Freuency of occur House value Percentage damage (X) Amount Tropical storm               0.14          1,500,000 0.01            15,000 Hurricane 1 0.08          1,500,000 0.05            75,000 Hurricane 2 0.05          1,500,000 0.1          150,000 Hurricane 3 0.01          1,500,000 0.2          300,000 Hurricane 4 0.01          1,500,000 0.7      1,050,000 Hurricane 5 0.01          1,500,000 1      1,500,000 No storm               0.70          1,500,000 0                     -  

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