EOM4 Test Q5 & Q9

[1695814]

couldn't find anything in the soa/fap forum...there's only like 8 threads left out there

anyway...is it okay/legal/ethical for me to post the entire question here? I hope so...

Module Test
You are the pricing actuary for XYZ Insurance Company in the product development area for one-year term insurance. For the next year you make the following assumptions:

Number of policies sold

20,000 policies (all assumed to be independent)

Average amount of insurance

$100,000

Total amount at risk

$2 billion

Weighted average mortality rate

0.7%

Expenses

6% of gross premium

You set the gross premium such the probability of total claims exceeding total gross premiums is 2.5%. This achieves XYZ Insurance Company’s target underwriting margin. What is the appropriate gross premium per average policy?

You are given the following values from the cumulative distribution function of a standard normal random variable:

z value

P(Z=z), Z ~ N(0,1)

1.645 95.0%

1.960 97.5%

2.325 99.0%

All I remember is that to standardize the rv you subtract the mean and divide by the standard deviation.

heeeeeeeeeeeeeeelllllllllllllllllllllllllp.

Spoiler:

the soa's answer is 816

[1695814]

...and I don't get Q9 either...

An insurance company has 1,000 endowment policies in force. Each policy has a face amount of $1,000 that is due to be paid in one year. The insurer has a total of $900,000 in assets backing these policies, all of which are due for reinvestment. The company has a choice of four investment instruments. The value of each investment follows a lognormal distribution with constant growth and volatility rates, as shown below:

/

Growth Rate (µ) Volatility Rate (σ)

Option A 10% 15%

Option B 12% 25%

Option C 14% 30%

Option D 16% 40%

Which investment option should the company select if it wants to maximize the probability of being able to meet its obligation on the endowment policies?

For a lognormal distribution, where St = the value at time t, Ln(St) is normally distributed with mean Ln S0 + (µ - σ2/2)t and standard deviation [sigma * square root of t].

Spoiler:

the soa's answer is C

[strategygamer]

Originally Posted by 1695814

All I remember is that to standardize the rv you subtract the mean and divide by the standard deviation.

yup.
z = (x - mu) / sigma
z = 1.96 (from your table)
therefore the 97.5th percentile = mu + 1.96 * sigma

mu = 0.007 * 100000 = 700
sigma squared = [e(x^2) - (e(x))^2 = (0.007 * 100000 * 100000) - (0.007 * 100000)^2] / 20000 = 3475.5
sigma = 58.95

x = 700 + 58.95 * 1.96 = 815.55