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**Martingales and arbitrage in multiperiod securities markets.**
*(English)*
Zbl 0431.90019

From the introduction: We consider some foundational issues that arise in conjunction with the arbitrage theory of option pricing. In this theory, initiated by Black and Scholes, one takes as given the price dynamics of certain securities (such as stocks and bonds). From these, one tries to determine the prices of other contingent claims (such as options written on a stock) through arbitrage considerations alone. That is, one seeks to show that there exists a single price for a specified contingent claim which, together with the given securities prices, will not permit arbitrage profits.

### MSC:

91G20 | Derivative securities (option pricing, hedging, etc.) |

91B26 | Auctions, bargaining, bidding and selling, and other market models |

60B05 | Probability measures on topological spaces |

### Keywords:

multiperiod securities markets; martingale measures; arbitrage theory; option pricing; contingent claim valuation
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\textit{J. M. Harrison} and \textit{D. M. Kreps}, J. Econ. Theory 20, 381--408 (1979; Zbl 0431.90019)

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