Some updates

Yes, the blog has been quiescent lately.  Here are some updates.



1. Moving On #1

I tweeted this out today after a prompt in an email.  This may or not explain the quiescence. Let's hope it does.

"In 2016 and 17 I was insanely productive on my quant ret-fin blog. In 2019? Not so much. I noticed a correlation that is represented in the attached chart. Infer what you will about my romantic relationships in 2016-17 and then in 2019" 

2. Moving On #2

If you read the blog closely you may have inferred that I was maybe suckered into moving to FL 11 years ago in an act of low-rent, malicious, bad-faith fraud. If so, you would have inferred correctly. My youngest is now 3.5 years from getting out of HS.  That means that I will start to borrow from blog-and-modeling time to donate to plan-to-move time.

3. Clarification on my WDT model

One of my mainstay instantiations of the blog is a piece of software I built to do simple simulations of "expected discounted utility of lifetime consumption" with some clarity on what happens during the period of time where wealth depletes before death.  This is a relatively reductive but useful model.  The description of what I did, however, is not entirely complete.  One thing that I fudged on was a wee bit of a hedge on the utility calc.  I kinked the function and did not really make that explicit in my cover of the topic.  If one were to be explicit it would look more like this although I'm not sure the notation is exactly correct:

where c(t) is consumption in time t and gamma is the coefficient of risk aversion. k is a floor I put under the utility function.  There is an equivalent kink for gamma = 1.  Here are a few thoughts on this.

• I did this mostly because the effects of infinite disutility are pretty pernicious and demand a coding response. 
• In theory people are not really ruined. Jobs are sought, family steps in, institutions of governmental or associative social services come to bear, banks are robbed, etc.  No one consumes at zero. Yaari touched on this in '65 though he spoke in Wealth terms: "some people think that the institutional framework makes it virtually impossible for a man in our society to die with a negative net worth. For this reason it is of interest to see what the consumer's optimal plan looks like given that the constraint S(T) >= 0 must hold with probability one."  Also, Dirk Cotton has covered an idea similar to this if I recall.
• It comports with my amateur common sense which counts for little.
• Patrick Collins in another context called stuff like this "not mathematically necessary" or arbitrary, which it is.  i.e., we are "off road."
• Call it what it is: a kluge or maybe a policy choice. This makes it an amateur distortion and a good reason to be skeptical of the analysis especially as it may or may not compare to other, especially utility-based, models.  
• If I had the courage of my convictions on being arbitrary, and I might in the future, I would maybe additionally modify the function to do something with the uncaptured negative features of very high consumption.  E.g., buying 2 lear jets adds very little to consumption utility on the margin but is unnecessary in some way and maybe has an impact on environment or culture that should take a hit in the individual model. That means there'd be a critical point where the function no longer rises monotonically.  Like I said, arbitrary and not mathematically necessary. TBD
• The effect is similar to the presence of lifetime income or social security except the utility "floor" is set here to a near-but-not-quite ruin level.  This is mostly relevant only for runs of the model where life income is absent.

The basic effect, in very rough illustration before we get to the last bullet, might look like this where the solid line is the kinked function and the dashed line is what a normal CRRA will buy you

You be the judge on whether this is naive, amateurish, and/or corrupt. I'm ok with it for now.