Nominal annuity allocation vs deferral - supplement to last post

This is an addendum to Annuity Allocation and Immediate vs. Deferral in a Lifetime Consumption Utility Context (the very last post).  I couldn't not throw in a 3D.

Without too much comment, this is a representation of the max value function (across all spend rates and allocations to risk) for each combination of (a) allocation to a nominal (fake, in-model) annuity between 10 and 50%  and (b) deferrals including: none(SPIA), to-70, 75, and 80. I skipped 85 since the numbers were not great at that age.

As before, this is not terribly universalizable and was made using some personal and fairly rigid choices for a set of parameters. You'd have to know those parameters and why I used them to get some more intuition on the output.  The link to the last post contains links to all of the past posts.

As before there is a overall maxima area around 30% allocation and deferral to 75 with the edges favoring a direction towards 20%/age75-80 and 40%/age70. The chances, however, that I will annuitize anything this year is still approaching zero.