If deaths are observed at age x where x = calender year of death - calender year of birth, which age category should we work with? Age next birthday?
Age Next Birthday. reason:- Let a person born on any date in the year 2000, and died on any date in the year (2000+i)........... x will be i. Now draw a timeline, you'll see on 1st Jan (2000+i) age next birthday is always be i.
Calendar year rate intervals are no longer on the CT4 syllabus. You only have to be able to deal with life year rate intervals.
IAI 2015 april's paper, ques(6) involves calendar year and policy year both: A life company writes a significant proportion of health insurance business. The premiums for the policy are based on age last birthday at the start of the policy. The policy covers multiple claims during the term i.e the policy does not exit on a claim, it only exits due to lapsation or the policy term getting completed. The company is interested in analyzing the morbidity experience and has asked its health team to collect suitable data for the investigation. The team has submitted the following data. hx number of claims at age x where x is defined as ‘Age last birthday on the policy anniversary prior to making the claim’ Px,t = Number of policies in-force as at 1st April classified as age x last birthday at time t (t = time elapsed from 1st April 2013), for the period from 1st April 2013 to 31st March 2015. i) Explain what is meant by a ‘rate interval’ and give the rate interval as per the above data. ii) Derive an expression for the central exposed to risk Exc of the analysis, clearly stating the assumptions made. The following is the summary of the data for ages 44 to 46 iii) Estimate μ45 and state the exact age to which the μ applies. i didnt get from the solution how to approximate the Px,t from the given one. And also the mu45 is the estimate for mu44.5!
Calendar year and policy year rate intervals are not in the CT4 syllabus so this question could not be asked on the UK CT4 paper. If the questions are asked in the Indian exams, here is my way of working through calendar year and policy year rate intervals... Construct an age line of half yearly points and put the rate interval anywhere on it comprising one year. Then DIE in the middle of the rate interval and go in search of where the x actually is. eg hx number of claims at age x where x is defined as ‘Age last birthday on the policy anniversary prior to making the claim. Put my pen in the middle of the rate interval I've just died, where is my last policy anniversary? Answer: six months ago (assuming policies are sold uniformly over any given year). So I move my pen, one notch (half-year) to the left (so my pen is now at the start of the rate interval.) Now at this point (where my pen is) I was x on my last birthday. On average, when is my last birthday? Answer: six months ago (assuming birthdays are uniformly distributed over any given policy year) So I move my pen, one notch (half-year) to the left (so my pen is now six months before the start of the rate interval.) This is where I write "x" with my pen. After this (so long as you are capable of adding and subtracting) you can fill in the age line. The rate interval goes from x+0.5 to x+1.5. q is always an estimate of what is written at the start of the rate interval, ie qx + 0.5 mu is always an estimate of what is written in the middle of the rate interval, ie mu x+1 This method always works so good luck with it! John
