I found some minor coding errors in my tool (remember it estimates -- in order to mimic the Kolmogorov equation -- the lifetime risk of ruin using the joint probability of: a) a lifetime net-wealth "ruin" process and b) a mortality process using gompertz math ) so I thought I'd do a more comprehensive test of the resulting code changes to see if there were any approximation weaknesses.
I created 96 test conditions by varying:
- net returns between .03 and .05
- std dev beween .10 and .20
- start age between 60 and 80
- Mode/dispersion of mortality pdf between 85/10 and 90/8.5
- spend rates from .03-.06
The result, when I did a simple point difference between the baseline K-equation and the approximation tool (I hope that's the right way) for the 96 conditions, was a mean and median of difference hovering around zero (good) and a standard deviation of less than half a point (pretty good). Min/max are both inside a 1 pt difference. I'm not sure yet if there are pockets of difference in there that matter but the higher "volatility" conditions seem to have a little more variance from baseline. Most of the variance, though, more likely comes from the fact that the lifetime process for a wealth fail is in fact a mini-sim with results that are a moving target so maybe the iterations can be nudged up a bit to fix that.
All in all I think I can call this a wrap. I not only successfully replicated a well known PDE with something way easier, I now have a way to explain the Kolmogorov PDE if I ever write up a draft 2 of what I wrote before on that. In general I think I have a much better idea of the basic concepts and processes behind ruin estimation which was one of the original goals I started out with in the first place.
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