I've been playing with this thing just for fun to see where it goes. The first versions were too discrete in it's approach to spending exploration and therefore a little unstable. Also I had only designed it for log utility (i.e., low or RA=1 in CRRA math). This increment of coding added RA > 1 where the formula is [C^(1-ra)-1]/(1-ra) if I recall correctly.
For this really fast, too-short, too-few-iterations run I flipped RA to 2. Not much of a change but: a) going up a bit in RA has convex and significant effects, b) in my own work a RA=2 is about how I behave based on what I see, and c) my opinion is that really high RA needs fewer models and more counselling. Think of it this way. If I wear a seat belt I am prudently risk averse. If I am an agoraphobic and never leave the house, I am risk averse and I need help. I have an unfounded opinion that over about RA=3 it starts to get a little odd, but that's just me.
Here is the set-up for this post:
- same as linked post in all respects
- both were told to start w 4% spend with sanction to find "better" based on a value function
- RA=2 not 1
- benchmarks are revised in this post. I only use two:
- The solved-for spend rate from a Kolmogorov model for life probability of ruin set to a constant 5% as a proxy for higher risk aversion. I think I used 10 or 20% before, I'd have to look. Recalc at each age assuming all else equal. The K model uses Gompertz math with mode = 88 and dispersion = 9.
- My adaptation of Evan Inglis' divide by 20 rule that adjusts by age and is roughly equivalent to a constant 5% fail risk in other models.
When we run the machine (I only did it a few thousand times because it's slow -- maybe 30 min per 1000 -- and I just wanted to see what shape of the curve is forming...I'll run it a bazillion later to see what happens), the policy table for "wealth == 1,000,000 constant at all ages," we get this, below, in Figure 1. The upper lines (blue) are what we already did for RA=1. The lower (green) is RA set to 2 along with the 2 benchmarks above. Some day I'll look at 3 and higher.
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| Figure 1 |
Discussion
Discussion later, I'm headed out of town. But: a) it trained itself up again at later ages, b) it has vaguely similar convexity, c) it is playing a similar game in response to higher risk aversion, and d) there is a big divergence at earlier ages.
On "d" my guess is that it has something to do with the difference between models, 1 that sees lifecycle (decumulation) consumption utility, and 2 that don't. I'll look at that later.
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