# Fundamental theorem of arbitrage-free pricing

- Fundamental theorem of arbitrage-free pricing
In a general sense, the fundamental theorem of arbitrage/finance is a way to relate arbitrage opportunities with risk neutral measures that are equivalent to the original probability measure.

**The fundamental theorem in a finite state market**

In a finite state market, the fundamental theorem of arbitrage has two parts. The first part relates to existence of a risk neutral measure, while the second relates to the uniqueness of the measure (see Harrison and Pliska):

#The first part states that there is no arbitrage if and only if there exists a risk neutral measure that is equivalent to the original probability measure.

#The second part states provided absence of arbitrage, a market is complete if and only if there is a unique risk neutral measure that is equivalent to the original probability measure.

The fundamental theorem of pricing is a way for the concept of arbitrage to be converted to a question about whether or not a risk neutral measure exists.

**The fundamental theorem in more general markets**

When stock price returns follow a single Brownian motion, there is a unique risk neutral measure. When the stock price process is assumed to follow a more general semi-martingale (see Delbaen and Schachermayer), then the concept of arbitrage is too strong, and a weaker concept such as No free lunch with vanishing risk must be used to describe these opportunities in an infinite dimensional setting.

**ee also**

*Arbitrage pricing theory

*Rational pricing

**References**

*M. Harrison and S. Pliska, (1981), Martingales and Stochastic integrals in the theory of continuous trading. Stoch. Proc. & Appl., Vol. 11, pp. 215–260.

*F. Delbaen, W. Schachermayer, (1994), A General Version of the Fundamental Theorem of Asset Pricing. Math. Annalen, Vol. 300, pp. 463–520.

**External links**

* http://www.fam.tuwien.ac.at/~wschach/pubs/preprnts/prpr0118a.pdf

*Wikimedia Foundation.
2010.*

### Look at other dictionaries:

**Fundamental theorem** — In mathematics, there are a number of fundamental theorems for different fields. The names are mostly traditional; so that for example the fundamental theorem of arithmetic is basic to what would now be called number theory. Theorems may be… … Wikipedia

**Arbitrage pricing theory** — (APT), in finance, is a general theory of asset pricing, that has become influential in the pricing of shares. APT holds that the expected return of a financial asset can be modeled as a linear function of various macro economic factors or… … Wikipedia

**Rational pricing** — is the assumption in financial economics that asset prices (and hence asset pricing models) will reflect the arbitrage free price of the asset as any deviation from this price will be arbitraged away . This assumption is useful in pricing fixed… … Wikipedia

**No free lunch with vanishing risk** — (NFLVR) is a no arbitrage argument. We have free lunch with vanishing risk if by utilizing a sequence of tame self financing portfolios which converge to an arbitrage strategy, we can approximate a self financing portfolio (called the free lunch… … Wikipedia

**Risk-neutral measure** — In mathematical finance, a risk neutral measure, is a prototypical case of an equivalent martingale measure. It is heavily used in the pricing of financial derivatives due to the fundamental theorem of asset pricing, which implies that in a… … Wikipedia

**Mathematical finance** — is a field of applied mathematics, concerned with financial markets. The subject has a close relationship with the discipline of financial economics, which is concerned with much of the underlying theory. Generally, mathematical finance will… … Wikipedia

**Monte Carlo methods in finance** — Monte Carlo methods are used in finance and mathematical finance to value and analyze (complex) instruments, portfolios and investments by simulating the various sources of uncertainty affecting their value, and then determining their average… … Wikipedia

**List of theorems** — This is a list of theorems, by Wikipedia page. See also *list of fundamental theorems *list of lemmas *list of conjectures *list of inequalities *list of mathematical proofs *list of misnamed theorems *Existence theorem *Classification of finite… … Wikipedia

**Master of Financial Economics** — A master’s degree in financial economics provides an understanding of theoretical finance and the underlying economic framework.[1] The degree is postgraduate, and may incorporate a thesis or research component. Programs are often a joint… … Wikipedia

**Outline of finance** — The following outline is provided as an overview of and topical guide to finance: Finance – addresses the ways in which individuals, businesses and organizations raise, allocate and use monetary resources over time, taking into account the risks… … Wikipedia