Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematical finance, a risk-neutral measure, equivalent martingale measure, or Q-measure is a probability measure that results when one assumes that the current value of all financial assets is equal to the expected value of the future payoff of the asset discounted at the risk-free rate. The concept is used in the pricing of derivatives.In an actual economy, prices of assets depend crucially on their risk. Investors typically demand payment for bearing uncertainty. Therefore, today''s price of a claim on a risky amount realised tomorrow will generally differ from its expected value. Most commonly, investors are risk-averse and today''s price is below the expectation, remunerating those who bear the risk.