Fundamental theorem of asset pricing

The fundamental theorems of asset pricing (also: of arbitrage, of finance), in both financial economics and mathematical finance, provide necessary and sufficient conditions for a market to be arbitrage free, and for a market to be complete. An arbitrage opportunity is a way of making money with no initial investment without any possibility of loss. Though arbitrage opportunities do exist briefly in real life, it has been said that any sensible market model must avoid this type of profit.^{[1]: 5} The first theorem is important in that it ensures a fundamental property of market models. Completeness is a common property of market models (for instance the Black–Scholes model). A complete market is one in which every contingent claim can be replicated. Though this property is common in models, it is not always considered desirable or realistic.^{[1]: 30}

Discrete markets

In a discrete (i.e. finite state) market, the following hold:^[1]

1. The First Fundamental Theorem of Asset Pricing: A discrete market, on a discrete probability space (Ω, ${\displaystyle \scriptstyle {\mathcal {F}}}$, ${\displaystyle \scriptstyle {\mathcal {P}}}$), is arbitrage-free if, and only if, there exists at least one risk neutral probability measure that is equivalent to the original probability measure, P.
2. The Second Fundamental Theorem of Asset Pricing: An arbitrage-free market (S,B) consisting of a collection of stocks S and a risk-free bond B is complete if and only if there exists a unique risk-neutral measure that is equivalent to P and has numeraire B.

더 많은 일반 시장에서

단일 브라운주의 움직임에 따라 주가 수익률이 상승할 때는 특유의 리스크 중립적 조치가 있다. 주가 프로세스가 좀 더 일반적인 시그마마팅게일이나 세미마팅게일을 따른다고 가정할 때, 차익거래의 개념은 너무 좁고, 이러한 기회를 무한한 차원적 환경에서 설명하기 위해서는 소멸위험이 있는 무료급식 금지와 같은 더 강력한 개념을 사용해야 한다.^[2]

참고 항목

• 차익거래가격론
• 자산가격결정
• 금융 경제 § 차익거래가 없는 가격 책정 및 균형
• 합리적인 가격

참조

원천

추가 읽기

• Harrison, J. Michael; Pliska, Stanley R. (1981). "Martingales and Stochastic integrals in the theory of continuous trading". Stochastic Processes and their Applications. 11 (3): 215–260. doi:10.1016/0304-4149(81)90026-0.
• Delbaen, Freddy; Schachermayer, Walter (1994). "A General Version of the Fundamental Theorem of Asset Pricing". Mathematische Annalen. 300 (1): 463–520. doi:10.1007/BF01450498.

외부 링크

• http://www.fam.tuwien.ac.at/~wschach/pubs/prepr0118a.pdf