Mar 29, 2018

Pseudo Annuity Boundary for Age 60 Male With 100k Lifestyle?

I took a shot here at trying to visualize a hypothetical series of future, inflation-adjusted, loaded, annuity prices for a 60 year old using an inflating 100k lifestyle over time along with updated mortality assumptions at each age.  The method I am using to price is this, except that I add a load of a(x)*(1+L) where L is 10%:
At t(1) in each series for each age "x," the tCx term is the 100k but inflated to each (x) by 3 or 4%. Then for t[1:(120-x)] for a given x, the tCx series is inflated at 3 or 4%.  tPx is extracted from the SOA IAM table with G2 extension to 2018 and the conditional probabilities are updated for each (x). w is 120.  Other than the load there are no other frictions modeled to help with one's confidence in any type of realism. The annuity discount "d" used to price a(x) is a not very happy assumption of a constant, average .03 but happy or not it makes my life easier to do so right now. The phrase "not a very happy assumption" was one I found in Yaari (1965) on page one where he made a reference to the "unhappy" assumption that consumer preferences were to be independent over time. I thought that his shift in tone by using language like that humanized an otherwise difficult and dry mathematical treatment of life-cycle quantitative econ; I was momentarily amused.


The result, if I got this right, is what I might consider a personal "annuity boundary" but rendered in a "unit" term of 100k (today) which I can then mentally scale down or up depending on the real lifestyle in play.  I just wanted to try to see this in semi-realistic terms to the extent that this can be considered realistic. Theoretically, I might use this kind of thing in a continuous management of an "actuarial" balance sheet along with my updated estimates of spending via stochastic present values to decide if I am vectoring towards some new kind of infeasibility condition in the near future.  I'm not sure if I would really do exactly that in my real life but conceptually I think it is not a totally flawed way to look at it. On the other hand I don't really know if you can even buy an annuity at 95. I haven't looked.

Charted out it would look like this which is in FV terms:




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