Infinitely Many Securities and the Fundamental Theorem of Asset Pricing

Balbás, Alejandro; Downarowicz, Anna

doi:10.1007/s00009-007-0121-2

Cited by 8 publications

(4 citation statements)

References 31 publications

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“…For example, in bond markets, zero-coupon bonds are parametrized by their maturities θ which is a continuous parameter. However, only a finite number of bonds are traded at the same time, see [22], [30], [3].…”

Section: The Modelmentioning

confidence: 99%

Robust fundamental theorems of asset pricing in discrete time

Chau

2020

Preprint

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This paper is devoted to the study of robust fundamental theorems of asset pricing in discrete time and finite horizon settings. The new concept "robust pricing system" is introduced to rule out the existence of model independent arbitrage opportunities. Superhedging duality and strategy are obtained. * This work is supported by Center for Mathematical Modeling and Data Science, Osaka University. We thank Masaaki Fukasawa, Miklós Rásonyi and Martin Schweizer for constructive comments on the earlier version of the paper.

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Section: The Modelmentioning

confidence: 99%

Robust fundamental theorems of asset pricing in discrete time

Chau

2020

Preprint

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“…It does not appear that in the setting of infinite-dimensional stochastic integration any sigma-martingale equivalence to a form of no approximate arbitrage has been proved in the literature. A related result is proved in [2], where the setting is discrete time and the number of assets is countable, but the FTAP does not extend in its original (discrete-time) form. Instead, no arbitrage is characterized by projective limits of projective systems of martingale measures.…”

Section: Fundamental Theorems Of Asset Pricingmentioning

confidence: 99%

Fundamental theorems of asset pricing for piecewise semimartingales of stochastic dimension

Strong

2014

Finance Stoch

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The purpose of this paper is two-fold. First is to extend the notions of an n-dimensional semimartingale and its stochastic integral to a piecewise semimartingale of stochastic dimension. The properties of the former carry over largely intact to the latter, avoiding some of the pitfalls of infinite-dimensional stochastic integration. Second is to extend two fundamental theorems of asset pricing (FTAPs): the equivalence of no free lunch with vanishing risk to the existence of an equivalent sigma-martingale measure for the price process, and the equivalence of no arbitrage of the first kind to the existence of an equivalent local martingale deflator for the set of nonnegative wealth processes.

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“…It does not appear that there exists in the literature any sigma-martingale equivalence to a form of no approximate arbitrage in the setting of infinite-dimensional stochastic integration. A related result is proved in [2], where the setting is discrete time and the number of assets is countable, but the FTAP does not extend in its original form.…”

Section: Fundamental Theorems Of Asset Pricingmentioning

confidence: 99%

Fundamental Theorems of Asset Pricing for Piecewise Semimartingales of Stochastic Dimension

Strong

2011

SSRN Journal

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This paper has two purposes. The first is to extend the notions of an n-dimensional semimartingale and its stochastic integral to a piecewise semimartingale of stochastic dimension. The properties of the former carry over largely intact to the latter, avoiding some of the pitfalls of infinite-dimensional stochastic integration. The second purpose is to extend two fundamental theorems of asset pricing (FTAPs): the equivalence of no free lunch with vanishing risk to the existence of an equivalent sigma-martingale measure for the price process, and the equivalence of no arbitrage of the first kind to the existence of an equivalent local martingale deflator for the set of nonnegative wealth processes.

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Infinitely Many Securities and the Fundamental Theorem of Asset Pricing

Cited by 8 publications

References 31 publications

Robust fundamental theorems of asset pricing in discrete time

Robust fundamental theorems of asset pricing in discrete time

Fundamental theorems of asset pricing for piecewise semimartingales of stochastic dimension

Fundamental Theorems of Asset Pricing for Piecewise Semimartingales of Stochastic Dimension

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