 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
 dsmith3 Member SOA AAA Join Date: Jun 2005 Location: Dallas, Texas Studying for Exam DP - ILA Favorite beer: Free Posts: 564 Multiple lives question

peewee,

This comes from ASM 36.20. For an insurance on (55:55) that pays a death benefit of 1000 at the moment of the first death, you are given:
(ii) Mortality on both lives follow de Moivre's law with w=100.
(iii) force of interest is .04

Calculate the net single premium for the insurance.

I know this is not a very difficult problem, especially in the single life. But with multiple lives the integral gets very ugly. Is there another way to do this problem other than integrals? Thanks. Have a great Easter weekend. #2 Steve Paris Note Contributor SOA   Join Date: Aug 2005 Location: FSU (Go NOLES!!) Favorite beer: Cold Posts: 135 Hey D-Rat,

Sorry for not checking this for a few days, but I spent this weekend at the beach.

Here's how I would do this problem (no evaluation of integrals):

The integral that would give this NSP is 1000 * Int(from 0 to 45) [v^t * t_p_xy * mu_xy(t)] dt. Notice that because of independence, t_p_xy = t_p_x * t_p_y, and mu_xy(t) = mu_x(t) + mu_y(t). So when you multiply t_p_xy * mu_xy(t), you'll get the sum of two terms: t_p_x * t_p_y * mu_x(t) + t_p_x * t_p_y * mu_y(t).

Now recognize that under DML, t_p_x * mu_x(t) = 1/(w-x) = 1/45 in this case. Likewise t_p_y * mu_y(t) = 1/45. So the sum of the two terms in the last paragraph is 1/45 * t_p_y + 1/45 * t_p_x = 2/45 * t_p_55 since both x and y are 55.

Factoring out the constant 2/45, we get the NSP = 1000 * 2/45 * Int(from 0 to 45) [v^t * t_p_55] dt. Now recognize the integral as being a(bar)_55 = (1 - A(bar)_55) / delta. Using DML, A(bar)_55 = 1/45 * a_angle45 = 1/45 * (1-e^(-45*.04))/.04 = .463723.

So I get NSP = 1000 * 2/45 * (1 - .463723)/.04 = 596.

P.S. Is this the manual's answer? Please let me know what their answers to the questions are from now on, so that I'll know if I've miscalculated something.
__________________
Steve Paris, Ph.D, ASA
paris@math.fsu.edu

 Thread Tools Search this Thread Show Printable Version Email this Page Search this Thread: Advanced Search Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded 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 08:30 AM.

 -- 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