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

doi:10.1016/0167-6687(92)90013-2

Insurance: Mathematics and Economics

Volume 11, Issue 4, December 1992, Pages 249-257

https://doi.org/10.1016/0167-6687(92)90013-2 Get rights and content

Abstract

Dalang, Morton and Willinger (1990) have proved a beautiful version of the Fundamental Theorem of Asset Pricing which pertains to the case of finite discrete time: In this case the absence of arbitrage opportunities already characterizes the existence of an equivalent martingale measure. The purpose of this paper is to give an elementary proof of this important theorem which relies only on orthogonality arguments. In contrast, the original proof of Dalang . uses heavy functional analytic machinery, in particular measurable selection and measure-decomposition theorems. We feel that the theorem (as well as its proof) should be accessible to a wider public and we therefore made an effort to keep the arguments as selfcontained as possible. In a final chapter we review and prove the necessary tools for our presentation of the theorem.

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

Abstract

J. Math. Econ.

J. of Math. Econ.

Approximate Completeness with Multiple Martingale Measures

On the fundamental theorem of asset pricing with an infinite state space

Journal of Mathematical Economics

The pricing of options and corporate liabilities

J. of Political Economy

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

Stochastics and Stochastics Reports

Representing martingale measures when asset prices are continuous and bounded

Math. Finance

A General Version of the Fundamental Theorem of Asset Pricing

On weak compactness in L1(μ, X)

Proc. Am. Math. Soc.

Hedging of Contingent Claims under Incomplete Information

On weak compactness in L¹(μ, X)