I think I do not really understand reserving. Taking the example of a profit test, the reserve at the start of the policy is always 0. This doesn't seem to make sense since there is a sum assured, so surely some funds need to be set aside at the start of the policy in case of death in the first year of the policy? I would have though that a prudent time 0 reserve would be the PV of the sum assured, but this does not seem to be how reserving works. Instead (perhaps in earlier chapters of the notes now) reserves usually take into account the probability of the event occurring, so if death does occur there is always a shortfall i.e. the reserve does not cover the sum assured. Then in a profit test we have the reserve at the end of year 1 being p_x 1_V , which I can see is interpreted as being 'the reserve of 1_V is only needed if the life survives the first year', but again this doesn't seem very intuitive. Please help!
Actually I think in one example in chapter 13, for a pure endowment policy that pays 1000 in 5 years, you can calculate the reserve at time 0 using the reserve basis as 1000*(1+ires)^-5. Further, if you want to calculate net premium reserve for a whole life assurance policy at t=0, use the formula 1 - a(subscript x+t)/a(subscript x), and at time 0, this will be zero (this is discussed in chapter 7 net premium reserves). This assumes the premium used in reserve calculation is calculated using equivalence principle. Therefore it is intuitive that the reserve at t=0 is zero as the EPV future benefits less EPV future income (reserve calculation) perfectly offset each other (given this is the equivalence principle at t=0). It gets trickier if the premium assumption does not apply, as with gross premium reserves. I dont think I have come across a reserve calculation question for t=0 but I my guess is the principle remains the same (EPV future benefits - EPV future income). Does it? To your second question, in my understanding reserves at say time = 2 are needed for those that have survived over year 1 and 2 with known probability of survival over that year. Those that died in the year dont need a reserve as the benefit for them is paid out. This is the idea behind reserves. To hold back profits, for those alive that may die in future. Further comments, questions welcome. I am here to learn as well!!
