Blogging Employee Benefits

January 6, 2006

Simply Stochastic

Filed under: Actuarial — Fuguerre @ 7:04 pm

Roll Model: Simulating a Savings Plan Account Balance in the January/February 2006 issue of Contingencies presents a relatively simple explanation of stochastic modelling of economic processes, in this particular instance with an eye toward the stochastic modelling being conducted by actuaries of the Social Security system. Whether or not the straightforward probabilistic approach used by far too many whizbang stochastic models truly give any better decision-making insight into something as complex as the Social Security system is never adequately addressed in the article. OK, yeah, the article had tight space constraints and needed to steer clear of arcane actuarial jargon so as to reach the more common audience that Contingencies pitches. Even so, it would not have taken more than a quick paragraph or two to focus on the difference between stochastic processes that have no dependency on time or on previous events or choices, versus those where the probability distribution function at time t+1 differs from that present at time t depending on the passage of time, the particular environment produced by the probabilities present at that prior time, and the choices made. So a stochastic Monte Carlo simulation of production over a short period (i.e., so wear and tear can be ignored for this exercise) of a widget with a relative stable, time-independent probability distribution function and a mechanical process that does not change the probabilities applied to the next widget depending on what had been done for the last widget differs quite conceptually and practically from a stochastic simulation of something like the interest rate climate, when too many blindly ignorant supposedly sophisticated models would continue to make the computer shirp merrily away spitting out some scenarios in the mix that blithely ignore that the system has produced negative interest rates with exactly the same future possibilities at hand as for the scenarios with ultra-high inflation-climate interest rates, worse yet with precisely the same blind responses by the investor or pension plan sponsor seen under either of those two extreme scenarios produced by the model. They seem to figure that as long as they average enough millions of scenarios, the fantasy behind any single one of those scenarios – even those not at the extreme – can be ignored.

And that’s not even to mention that far too many of these models use probability distribution functions that presume independence that does not exist in the thing being modeled, on top of a particular type of distribution function that does not reflect the reality of the thing. Like interest rate futures beyond perhaps a moment into the future can truly be modeled using a normal curve?

Since the article itself does admit that it does not speak directly to the particular stochastic methodologies in use by the Social Security Administration itself, it’s impossible to use that article as a springboard for any appraisal at all of the very development that seems to have led to the article. Leaving me completely in the dark as to what the article was attempting to communicate. If nothing beyond a mere glance at the simplest side of stochastic modeling, then I find that as dangerous as the pile of hotly marketed but quite poorly designed stochastic models building up around pension plans and other financial instruments like a cloud of thick smoke and a pile of smudged mirrors. Too many already have run those simple stochastic models for their financial instruments thinking that magic words like Monte Carlo get them something more meaningful than the supposedly rigid deterministic lines that might have served them better in the end.


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