Hi, I have searched the forum and there seem to be very few discussions on this topic. May be it was just me who couldn't get my head round this matter, so I hope you can kindly bare with me . 1) Can someone help explain what is the difference between aq and ad in the definition of the North American method under section 2.1 of chapter 24? In the example that follows immediately after the definition, aq don't really seem to be anyway in sight. Is the fundamental idea behind the North American method just to assume a double decrement for those who do not take up the option? 2) In example 1 of page 15 of the chapter, I still don't get why there is an A multiplied to the second summation of the expected pv of benefits. Actually, shouldn't there is an A for the first summation sign as well? This might be a very easy answer to most of you, but somehow i just can't get my head round. Perhaps it was because I misunderstood what ad stands for here. 3) My last question will be the use of ultimate and select mortality. On page 17 of the chapter, why is the A60 term not A[60] since in the question it reads: standard mortality will be AM92 select and only those mortality after taking the option will be ultimate? It confuses me even further in the mortality assumptions on page 18, that says the formula for EPV assumes that lives who do not take up the option will experience ultimate mortality. Isn't this exact opposite to what was given in the question? It will be brilliant if someone can help explain a bit when to use ultimate and when to use select... Thank you very much for your time. Your help will be very much appreciated as I have been stucked on this chapter for quite some time already.
We use aq and ad in multi decrement tables in the same way as we use q (the probability of death) and d (the number of deaths). So aq is the number of deaths divided by the number of lives, ie aq = ad / al. The example chooses to write ad / al, it could easily have been written using aq instead. We're looking to get the probability that someone dies. They can either die before they take the option (using probability aq = ad /al) or after they take the option. If they take up the option we first need the probability that they take the option from the multi-decrement table. This is given by (aq)w = (ad)w / al. We then must multiply by the probability that having taken the option at the end of year t, that they then go on to die - the A factor calculates the present value of this using a single decrement mortality table in the usual way. The lives were all underwritten when they took out the policy aged 55. However, the select period runs out after 2 years, so these lives will all be ultimate when they reach 57. So at age 60 there will be two groups: those who don't take the option will be 60 ultimate as expected, those who do take the option will be rated up an extra 10 years. The lives that do not take up the option will experience ultimate mortality after the date of the option because the select period has already finished. All lives experience select mortality for the first two years of the contract. I hope this helps clear up the confusion. Best wishes Mark
Thanks so much Mark! Sorry my reply comes a bit late. The only thing I am uncertain now is why mortality becomes ultimate after 2 years? Is this a universal rule or does this 2 years vary between question to question? sorry a lot of question, but thanks.
Hi The select period depends on the mortality table. In this example the question is using AM92 Select, which has a select period of 2 years. Best regards Lynn
