# Good ways to select best decision among N decisions, each with a profit/loss distribution? [closed]

I'm working on a problem where an asset owner (e.g., owner of a factory, power plant, etc.) can take a number of possible decisions (say 10). Each of those 10 decisions entails certain actions, but the profitability of those decisions is not known in advance (because of uncertainty in a number of the underlying variables). Empirical distributions of the unknown variables can be derived, and the profit/loss distributions can be computed for each of the 10 possible decisions.

What would be some of the standard ways of deciding which decision was best? Each profit/loss distribution has its own mean, standard deviation, percent of the curve which is negative, worst case scenario, best case scenario, etc. Is there a good standard way to make this comparison?

• Ah, I should clarify: does the owner take one of these possible ten decisions or does the owner make ten decisions, each with its own set of possible actions? Aug 8, 2020 at 0:44
• The former. The decision space is really continuous, but in the first step of the analyses I've effectively discretized those decisions into, say, 10 different ones. Aug 8, 2020 at 14:47

This looks like a classic real options problem. Essentially, each decision is an option which will be chosen strategically: the owner will chose a vector of actions from all possible actions, $$A\in\mathcal{A}$$, that maximizes expected utility given the distributions of key variables and outcomes.