Waiting for my DIA vs shifting longevity expectations

In this post I am wondering about the idea of waiting after my current  age (59) to hedge out longevity risk (after, say, age 85) with a deferred income annuity, a tool I know from academic papers and my own simulation that would enable me to increase consumption now for a level of risk that could be similar to that which might be held before a DIA purchase. Then I want to throw that "waiting idea" against the idea of longevity expectations increasing in the future due to something like med-tech innovations, something that has already been going on for a while now.  That would make the purchase of a DIA in the future relatively more expensive to the extent that insurers have not already figured this out...which they have. The Society of Actuaries already does something like this by providing a projection factor against its annuitant mortality tables.  Since I haven't figured out how to do that projection factor yet I'll try to look at this a different way.



I have seen somewhere (I can't put my finger on the link so take this with a grain of salt) that changes in longevity (so far) have mostly affected the mode of the longevity distribution rather than shifting the terminal age expectation. So the modal value of a longevity distribution might shift from 90 (that's an example very roughly based on SOA IAM tables for men around my age) to 95 (I made that up) but age 120 is still a rough outer boundary.  No one is living to 200 yet.  In pdf form it might look like this.

(the right chart has a y axis from 0 to 1; I accidentally chopped that off)

Now, like a previous post, I want to project out the estimated cost of a DIA if I wait until 65 or 70 or 75 etc... to buy it.  But this time I'll price a second time by shifting the modal expectation out a little bit (not scientifically, just moving it arbitrarily) at each of the future ages.  My guess is that if I could use the SOA projection factor the right way I would achieve something similar.  I guess this just means that the way I have been estimating future DIA costs is wrong by being too low.  This doesn't really matter since I am just illustrating all of this to myself.  My menagerie of other unrealistic assumptions includes no inflation, taxes, investment expenses, insurance loads, etc. so how realistic can this be anyway?

Here is what I came up with.

Blue lines - at each future age the estimated age 86 DIA cost for 100k in income. Upper uses a 2% discount rate the lower a 4%. The dotted blue line is a 3% discount right in the middle.

Solid green lines - the "unspent" premium grown at a constant rate (5% lower, 7% upper). Note: these are the growth amounts to age 85 from each age on the x axis. These are based on the dotted blue line

Dotted red line - the same as the dotted blue line but with the shift in modal mortality expectation over time.

Dotted green lines - same as the solid green lines but based on the dotted red.

Follow all that? Here is what it looks like

The assumptions are so bogus here that one can't really make any hard conclusions from any of this.  On the other hand, depending on one's capital market and medical progress assumptions, there might be a case for not waiting forever if one likes the idea of hedging.  I'll have to think about that. And ask an actuary.