Some effects of longevity assumptions on ruin estimates

In shaking out my lifetime ruin approximator tool, the one that mimics the Kolmogorov differential equation for evaluating the lifetime probability of ruin (LPR), I had forgotten to look at the effect of longevity assumptions on ruin estimates.  I know from some past posts that, for a 60 year old, if I plug in mode (M) and dispersion (b) parameters of 85 and 10 it more or less closely fits the Soc Security life table for someone my age (keep in mind that that is a "hacker close fit" not an actuarial science close fit) and that the parameters 90 and 8.5 roughly fit a curve derived from the Society of Actuaries Annuitant mortality table for someone my age.  The former can maybe be characterized as an average expectation across all of us while the latter is an expectation for a generally wealthier and theoretically healthier cohort that self-selects themselves into annuities.  They tend to live longer, hence that becomes a "real world" conservative assumption, data-set or baseline.

I'll use those two assumption sets (SS and SOA)  as my boundaries for an "average" longevity assumption and "conservative" longevity assumption.  Or at least for when we are working with stochastic longevity.  In real life I often use a fixed age of 95 or more if I want to be both simple and hyper-conservative.


I wanted to see what happens visually between the boundaries as well as to see the shape of the change in the ruin estimate as the estimate gets more conservative.  Since I had no other sciency stuff to back me up I just set up a table with a linear interpolation of Mode and Dispersion between the two boundaries. Maybe not legit but it gets me there.  The table looks like this:

	age	M	b
Average	60	85	10
	60	86	9.7
(in between)	60	87	9.4
	60	88	9.1
	60	89	8.8
Conservative	60	90	8.5

When I run those 6 scenarios, the effect on LPR looks like this with the boundaries in blue and the in between assumptions in dotted grey (is it grey or gray? 60 years and I still haven't figured it out):

The shape of the change in ruin rates looks like this below. Some of the shape may come from the fact that I was winging it from the linear interpolation rather than doing more careful actuarial modelling (I hope I mentioned that I am not an actuary).  The least we can say is that risk goes up if we expect to live longer but we already knew that. Next time, if I ever do this again, I'll push the boundaries out a little to see of if it looks like the curve really is bending on either end with diminishing changes to risk. Right now I can't tell very well.  On the other hand, how far in practical common sense terms can I go? This is probably the meat of many people's assumption range (when using stochastic longevity and distributions, that is...again).

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other assumptions:

- age 60

- 8% returns, 10% std dev

- -4% hit on returns for inflation fees taxes
- 4% constant spend

- 10000 iterations of the mini-sim for portfolio longevity