"Risk is often defined by the probabilities of possible future outcomes, be they the tossing of coins, the rolling of dice or the prices of assets at some future date. Uncertainty exists as the possible outcomes are many and the actual outcome that will eventuate is not known. This uncertainty is resolved when at some future time the actual outcome becomes known. The risk may be valued statistically at its expected value or in a market at the current price to be paid or received for acquiring or delivering a unit of currency on the resolution of the risk. The market value is also understood to be a discounted expected value under altered probabilities that reflect prices of events as opposed to their real probabilities. By construction the value of a risk is hence a linear function on the space of risks with the value of a combination being equal to an equivalent combination of values. As a consequence value maximization is not possible as non constant linear functions have no maximal values. Optimization becomes possible only after introducing constraints that limit the set of possibilities"--