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Concept# Risk-neutral measure

Summary

In mathematical finance, a risk-neutral measure (also called an equilibrium measure, or equivalent martingale measure) is a probability measure such that each share price is exactly equal to the discounted expectation of the share price under this measure.
This is heavily used in the pricing of financial derivatives due to the fundamental theorem of asset pricing, which implies that in a complete market, a derivative's price is the discounted expected value of the future payoff under the unique risk-neutral measure. Such a measure exists if and only if the market is arbitrage-free.
A risk-neutral measure is a probability measure
The easiest way to remember what the risk-neutral measure is, or to explain it to a probability generalist who might not know much about finance, is to realize that it is:
# The probability measure of a transformed random variable. Typically this transformation is the utility function of the payoff. The risk-neutral measure would be the measure co

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