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# Local Martingales And The Fundamental Asset Pricing Theorems In The Discrete-time Case

J. Jacod, A. Shiryaev

Published 1998 · Computer Science, Mathematics

Abstract. This paper is devoted to giving simpler proofs of the two fundamental theorems of asset pricing theory, in iscrete-time and finite horizon: namely the no-arbitrage theorem, and the market completeness theorem. Some elementary but apparently new results are also given on discrete-time martingale theory, and in particular a new condition for a local martingale to be a martingale.

This paper references

10.1007/978-3-540-31299-4_9

A general version of the fundamental theorem of asset pricing

F. Delbaen (1994)

10.1080/17442509008833613

Equivalent martingale measures and no-arbitrage in stochastic securities market models

Robert C. Dalang (1990)

10.1016/0022-0531(79)90043-7

Martingales and arbitrage in multiperiod securities markets

J. Harrison (1979)

Arbitrage et lois de martingale

C. Stricker (1990)

10.1016/0167-6687(92)90013-2

A Hilbert space proof of the fundamental theorem of asset pricing in finite discrete time

W. Schachermayer (1992)

10.1080/17442509408833943

Equivalent martingale measures and no-arbitrage

Leonard Rogers (1994)

10.1007/BFB0084157

Pathwise approximations of processes based on the fine structure of their filtrations

W. Willinger (1988)

10.2307/2329081

Dynamic Asset Pricing Theory

D. Duffie (1992)

10.2307/1427371

THE ANALYSIS OF FINITE SECURITY MARKETS USING MARTINGALES

M. Taqqu (1987)

10.1137/1139038

No-Arbitrage and Equivalent Martingale Measures: An Elementary Proof of the Harrison–Pliska Theorem

Yu. M. Kabanov (1995)

10.1016/0304-4149(81)90026-0

Martingales and stochastic integrals in the theory of continuous trading

J. Harrison (1981)

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10.1215/17358787-3750133

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D. Bartl (2019)

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10.1007/S10203-003-0040-Z

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