Necessary and sufficient conditions for a market to be arbitrage free and complete
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. [1] Though arbitrage opportunities do exist briefly in real life, it has been said that any sensible market model must avoid this type of profit.[2]: 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.[2]: 30
^ Varian, Hal R. (1987). "The Arbitrage Principle in Financial Economics". Economic Perspectives. 1 (2): 55–72. JSTOR 1942981.
^ abPascucci, Andrea (2011) PDE and Martingale Methods in Option Pricing. Berlin: Springer-Verlag
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illiquid. Schachermayer, Walter (November 15, 2002). "The FundamentalTheoremofAssetPricing under Proportional Transaction Costs in Finite Discrete Time"...
needed] Schachermayer, Walter (November 15, 2002). "The FundamentalTheoremofAssetPricing under Proportional Transaction Costs in Finite Discrete Time"...
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