Choosing Among Decisions with Uncertain Profit and Loss
Summary
The document frames a decision problem in which an asset owner compares possible actions using a profit-and-loss distribution for each. The distributions may be estimated from empirical distributions of uncertain inputs, and can differ in expected profit, dispersion, downside frequency, and extreme outcomes. The question is how to rank these alternatives when no single outcome measure captures every concern.
The answer treats each action as a real option and proposes choosing the action that maximizes expected utility. For an owner with ample capital and little concern about risk, expected profit may be an appropriate objective. A risk-sensitive owner can instead penalize risk, measured using a suitable risk metric. The answer also points toward stochastic optimization and references introductory material on real options. It does not prescribe a specific utility function, risk measure, or calibration method, so the preferred decision depends on the owner’s capital constraints and risk preferences.
Key ideas
- Represent each available action by its uncertain profit-and-loss distribution.
- Choose among actions by maximizing expected utility over possible outcomes.
- Expected profit can be a suitable objective when the owner can tolerate the associated risk.
- A risk penalty can reflect limited capital or concern about downside outcomes.
- Stochastic optimization and real-options analysis are relevant frameworks for structuring the choice.
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Full text
# Good ways to select best decision among N decisions, each with a profit/loss distribution?
# Good ways to select best decision among N decisions, each with a profit/loss distribution?
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?
## Answer by kurtosis (score 1, accepted)
https://quant.stackexchange.com/a/57194
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.
If the owner is well-capitalized, maximizing the expected value of profit would be sensible. Some owners might not have infinite cash or might be worried about risk; in that case it would make sense to maximize the expected profit minus some penalty times the risk (which could be measured in many ways).
For more on real options, you might benefit from reading the introductions by Haugh and Pindyck. Also, you should consider solving such problems with stochastic optimization. Hannah has some excellent notes on that and a more complete reference would be Birge and Louveaux.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.