While it is generally agreed that risk management is an essential component in any major business decision, managers don't necessarily know how to incorporate risk management in a decision-making framework. This is where stochastic optimization delivers value.
The key feature that distinguishes stochastic optimization from other methodologies, such as simulation models and expected value scenario analysis, is its ability to directly include risk in the optimization process, thereby incorporating many complex market uncertainties into a single recommended course of action - a course that can be adapted over time.
Consider, for example, the task of deciding whether or not to ramp up a combined-cycle plant on any given day. Actual on-peak electricity prices will not be known until they occur, so the ramp up decision must be made in advance with imperfect information.
In the stochastic optimization framework, the recommended decision will not only consider the probability that prices will be sufficient to profit, but also that the operating strategy can be adapted if markets do not pan out, that is to say, the unit can be ramped down. In a sense, the optimal strategy will include an insurance policy, so that it will work well under different scenarios.
Extending this concept to the entire portfolio, day-to-day decisions will be recommended that are flexible and well hedged. The manager is able to specify constraints on different measurements of risk, thereby dictating whether the deployment strategy should be aggressive or conservative.
Other methodologies do not offer this advantage. For instance, the expected value scenario analysis is deterministic by nature. It replaces uncertainties by their expected values. As a result, it may recommend the purchase of a single option that has the highest expected return which is obviously not a wise risk management strategy.
Stochastic optimization implies that future decisions are taken with respect to the future outcome of uncertain impacts and are matched to today's unique decision to be made. This adaptive decision making is also known as rebalancing or correcting today's decision with respect to the future realization of uncertainties.
Obviously, if one calculates profit and loss (PnL) along a particular scenario path, PnL is not only derived from what price, demand or resource evolution this scenario path represents, but also what decisions are to be made in response to this evolution. Stochastic optimization therewith improves risk measurement and management by incorporation of the adaptive decision process into PnL calculations. The distribution function of PnL results with significantly higher accuracy, whereby more reliable Value at Risk numbers can be derived as opposed to Monte-Carlo-Simulation.
The described approach towards risk management allows for more accurate PnL distribution functions and VaR values, because optimal future responding decisions in various scenarios are taken into account.
Therewith, stochastic optimization is in particular appropriate to support strategic decision making. Different corporate strategies, such as increasing forward trading volumes or applying different plant maintenance plans can be represented in the mathematical model. Optimization then results different PnL distribution functions that easily allow for the identification of the best corporate strategy.
