Actuarial Outpost > SoA EOM4 Test Q5 & Q9
 Register Blogs Wiki FAQ Calendar Search Today's Posts Mark Forums Read
 FlashChat Actuarial Discussion Preliminary Exams CAS/SOA Exams Cyberchat Around the World Suggestions

#1
11-13-2008, 11:42 PM
 1695814 Member SOA AAA Join Date: Aug 2002 Studying for FSA Financial Reporting Favorite beer: Root Beer Posts: 23,102
EOM4 Test Q5 & Q9

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...

Quote:
 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:
__________________
.
[this space for rent]
#2
11-14-2008, 12:06 AM
 1695814 Member SOA AAA Join Date: Aug 2002 Studying for FSA Financial Reporting Favorite beer: Root Beer Posts: 23,102

...and I don't get Q9 either...
Quote:
 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:
__________________
.
[this space for rent]
#3
02-16-2009, 03:29 PM
 strategygamer Member Join Date: May 2007 Studying for FAP Posts: 2,732

Quote:
 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
__________________
http://www.boardgamegeek.com

 Tags mod4

 Thread Tools Display Modes Linear Mode

 Posting Rules You may not post new threads You may not post replies You may not post attachments You may not edit your posts BB code is On Smilies are On [IMG] code is On HTML code is Off

All times are GMT -4. The time now is 04:51 PM.

 -- Default Style - Fluid Width ---- Default Style - Fixed Width ---- Old Default Style ---- Easy on the eyes ---- Smooth Darkness ---- Chestnut ---- Apple-ish Style ---- If Apples were blue ---- If Apples were green ---- If Apples were purple ---- Halloween 2007 ---- B&W ---- Halloween ---- AO Christmas Theme ---- Turkey Day Theme ---- AO 2007 beta ---- 4th Of July Contact Us - Actuarial Outpost - Archive - Privacy Statement - Top