Putting it all together: a wealth depletion time "utility simulator"

Over the last month or two I've been playing around with a spreadsheet that helped me look at the concept of wealth depletion time and the utility of lifetime consumption in a situation where consumption is forced to whatever income is available when a nest egg runs dry.  I thought I would take that simple spreadsheet instantiation and now try to put together almost all the pieces of retirement finance that I've been working on for a couple years in a more complete and robust way. And actually I think it's kind of neat how a ton of what I've learned over three years comes to an almost unified point in this effort[1].  To do all this I had to leave the deterministic spreadsheet (fixed returns, probability weighted lifetime) behind and go into simulation mode (randomized returns and lifetime as random variable) in R.

I'm not quite done but I have maybe 80% of the stub of a decently interesting simulator (what is this? my 9th or 10th so far?). I have some more work on the core and some additional features to complete but I thought I'd take a break and pass along what I am doing for the interested (are there any?).  Fwiw, there is no real purpose for any of this. This is mostly just to do it and for me to learn a little bit. I suppose I could use the tool on my own data and retirement process but I don't get nearly this complex in my own efforts.  Certainly this is not a commercial endeavor.  Unless, of course, you want to pay me.  Then it is. 

The basic idea looks like this:


"Expected discounted utility of lifetime consumption" Simulator, version 1

E[V(c)]	Expected value of discounted utility of lifetime consumption
	Expected because lifetime T is a random variable
	discounted utiles are summed over simulated life and averaged over sims
c(t)	custom spend path (e.g., constant or other like trend, inflections, rules[pending])
	not explicitly optimized
	snaps to available income at wealth depletion at some time t
	initial state = $x
S	Number of simulation iterations (say 10 or 20k)
T*	random lifetime variable generated using SOA table for given start age
k	subjective discount rate on utiles expressing some time preference
	time preference is symmetrical/exponential in this model
g()	constant relative risk aversion utility of consumption function
	gamma ≠ 1: CRRA utility with a constant: (c(t)^(1-g) - 1)/(1-g)
	gamma = 1: log utility of c(t)
income	1. inflation adjusted social security starting at age ____
	2. private inflation adjusted "bought" annuity income:
	- conceptual infl adj annuity purchaseable at time t/age x
	- subject to price <= available wealth at time t
	- depletes wealth by purchase price
	- priced using SOA conditional probabilities at time t/age x
	- priced using constant spend based on custom spend at time t
	- no reference whatsoever to what is realistic product in current market
wealth	initial state = $x
	return generation is either:
	- normally distributed with mean m and sd s, or
	- fat tailed distribution using a gaussian mix of two normal distrb[pending]
	Net wealth at time t = w(t-1)*(1+r) + income - spend
	Depletion can occur at any time t to T

[1] There are a bunch of posts on this on this site with references to the original work of others. Search WDT or "wealth depletion" in the search bar. Note that it is entirely possible that I got the math and economics wrong in which case I hope a compassionate quant will whisper in my ear that my econ-zipper is down.