×

zbMATH — the first resource for mathematics

Equivalent martingale measures and no-arbitrage in stochastic securities market models. (English) Zbl 0694.90037
Summary: We characterize those vector-valued stochastic processes (with a finite index set and defined on an arbitrary stochastic base) which can become a martingale under an equivalent change of measure. This question is important in a widely studied problem which arises in the theory of finite period securities markets with one riskless bond and a finite number of risky stocks. In this setting, our characterization gives a criterion for recognizing when a securities market model allows for no arbitrage opportunities (“free lunches”). Intuitively, this can be interpreted as saying “if one cannot win betting on a process, then it must be a martingale under an equivalent measure”, and provides a converse to the classical notion that “one cannot win betting on a martingale”.

MSC:
91G80 Financial applications of other theories
60G44 Martingales with continuous parameter
91B24 Microeconomic theory (price theory and economic markets)
PDF BibTeX XML Cite
Full Text: DOI