When calculating Total DSAR, why do I need to deduct the reserve of the person who died in this year? Didn’t we already take it into account when estimating reserves(567000) at end of 2017?
Hi, The 576,000 is an actual reserve held for all of the policies in force at the end of the year (imagine this as a number that the company's system generates at the end of the year). In our standard mortality profit questions we work out the reserve that would be held IF a life (/all of the lives) survives the year. Therefore, to convert the information given into the question into our usual workings we take the reserves for all of the lives that survived (576k) and add in the reserves that would have been held for the two policies that did not make it to the end of the year. This type of question allows us to drop the usual "all lives are the same age and have the same mortality" because if we have a reserve figure for the whole portfolio then we can take these two policies with different start dates, ages, sum assured and still work out the mortality profit. In that way, I suspect it's far more true of real-life calculations. Hope this helps. Joe
I don't quite get it. As far as I know after reading Chapter 19、20、27, the reserve is the expected amount V calculated by the company after calculating the future cash flow CF, which includes expected death costs, expected surrender costs, and the difference between insurance premiums and expenses. Didn't the company anticipate that someone might die this year, and therefore take a portion of these expected death benefits as a reserve, hoping to just get even and not use the money for other purposes? If according to the answer, it feels as if one more person dies and another reserve is required, so the original deposit (567000) seems to be different from what was taught in chapters 19 and 20?
What I mean is that the annual reserve after other necessary expense is reserved to cover the benefit of the expected number of deaths, and this is the case every year. The company hopes that right up to the last death of the policy it will correspond to expectations.
I think you might be thinking the 576k is an expected reserve? In profit testing we work out expected reserves at the end of each year by multiplying the reserve we would hold if a policy is in force at the end of the year by the probability that the policy remains in-force for the year in question. Mortality profit questions are based on actual reserves a company would hold if all lives survived. In regular mortality profit questions we do S-(t+1V + R) for one policy and then we end up scaling it for the whole portfolio by multiplying by n, the number of policies, for expected death strain and actual death strain. We work out t+1V as if the life IS alive at time t+1 and then take the expected present value of the future benefits + expenses - premiums at that time. Our death strain at risk then represents the extra money we would need to find (or money we can release) if the life dies during the year. If we're thinking about mortality and a death benefit then one of two things happen at the end of the year. If the life survives we set up the reserve for them, if they die we have to pay out the sum assured. E.g if t+1V=10,000 and S=70,000 then when a life dies we make a 60,000 loss because we have to pay out 60,000 more than the reserve. We would have set up a reserve of 10k but now we have to pay out 70k. Over a portfolio of policies expected death strain is DSAR * n * q_x+t = (S*n - t+1V*n - R*n) * qx The bit in the brackets is total sum assured - total reserve we would hold if everyone survives - total survival benefit at end of year. Total sum assured is given in the question but total reserve we would hold if everyone survives is missing. We have the reserve for all policies that DID SURVIVE so it's missing the reserves for the two policies where the policyholder dies. So we manually add their reserves in and then we have the total reserve that would be held at the end of the year if all lives survive. We can perhaps use a silly example to work out why not adding the reserve in would be wrong. Imagine we have two policies. One has a sum assured of 200k over the year and t+1V=120k, the other has a sum assured of 20k and t+1V = 5k. Now if the first policyholder dies then at the end of the year we would only hold the reserve for the policyholder who is alive. So the actual reserve held at the end of the year is 5k. You might then calculate the total death strain as 220k-5k = 215k. This suggests that if both lives die we make a 215k loss. However, that's because we've ignored the reserve we would have held if the first policyholder survived. In actual fact the total death strain is 220k - 125k = 95k. The expected death strain would be 95k x q_x+t. The actual death strain is the 80k extra we've had to pay out over the reserve for the first policyholder. Does this make it any clearer? Joe
