Multiperiod problem with actuarial issues, in a multidimensional scenario matrix.

From Tackling the 'Nastiest, Hardest Problem in Finance' by Barry Ritholtz. Ritholtz is talking to William Sharpe.

Consider some of the most challenging problems in finance: the equity-premium puzzle; binomial-option pricing models; do zero interest rates spur inflation or damp it; are stocks cheap or overpriced?

Challenging as those may appear, none compare to what Nobel laureate William Sharpe, 82, calls "decumulation," or the use of savings in retirement. It is, he says, “the nastiest, hardest problem in finance.”

Just consider that this is coming from the man who figured out how to price portfolios via the capital-asset-pricing model, and how to measure risk via the “reward to variability ratio,” or what has come to be known as the Sharpe ratio.

I frequently talk about the challenges of decision-making and forecasting in dynamic complex chaotic multi-causal systems with hidden feedback loops, logarithmic scaling, and tipping points. Sharpe has a briefer terminology that covers much the same base:

Many financial planners use a simple rule of thumb: withdraw 4 percent a year from your savings until you either die or run out of money. This one-size-fits-all solution is suboptimal for a reality where the potential outcomes are almost infinite, or as Sharpe describes it, a “multiperiod problem with actuarial issues, in a multidimensional scenario matrix.”

Read the whole thing for a great example of how a conceptually easy exercise balloons into an essentially infinite range of outcomes. In this case, Sharpe's model is only looking at six variables on the financial return side of the equation and it is already impossibly complex. He doesn't tackle the demand side of the equation where retirees might need variable financial flows in their retirement years.