Projective system approach to the martingale characterization of the absence of arbitrage

Balbás, Alejandro; Mirás, Miguel; Muñoz-Bouzo, María J.

doi:10.1016/s0304-4068(02)00036-8

Cited by 8 publications

(16 citation statements)

References 17 publications

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“…In [2], Balbás et al have used a projective system of measure spaces to obtain a measure corresponding to a no-arbitrage system of prices. As in our method, they also need to expand the market state space in order to obtain the measure.…”

Section: Introductionmentioning

confidence: 99%

Pricing functionals and pricing measures

Koopman¹,

Sengupta²

2008

COSA

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Abstract. We demonstrate how pricing functionals give rise to pricing measures, using a time-independent framework. For infinite market state spaces, the Gel'fand spectral theory for C * -algebras is used to obtain the pricing measure. Pricing functionals with additional market information are shown, within this model, to be given by conditional expectations. Our approach is time-independent, and the usual martingale property of prices appears as a special case in our method.

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Section: Introductionmentioning

confidence: 99%

Pricing functionals and pricing measures

Koopman¹,

Sengupta²

2008

COSA

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“…Balbás et al [4] have shown that it is possible to solve the counter-example of Back and Pliska [2] without drawing on free lunches. They characterize the arbitrage absence in dynamic discrete time pricing models.…”

Section: Introductionmentioning

confidence: 99%

“…However, for any finite subset of trading dates one can find projections of both measures that are equivalent, and there are Radon-Nikodym derivatives in both directions. Balbás et al [4] use this property to introduce the concept of "projective equivalence" of probability measures.…”

Section: Introductionmentioning

confidence: 99%

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Infinitely Many Securities and the Fundamental Theorem of Asset Pricing

Balbás

Downarowicz

2007

MedJM

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Abstract. Several authors have pointed out the possible absence of martingale measures for static arbitrage free markets with an infinite number of available securities. Accordingly, the literature constructs martingale measures by generalizing the concept of arbitrage (free lunch, free lunch with bounded risk, etc.) or introducing the theory of large financial markets. This paper does not modify the definition of arbitrage and addresses the caveat by drawing on projective systems of probability measures. Thus we analyze those situations for which one can provide a projective system of σ−additive measures whose projective limit may be interpreted as a risk-neutral probability of an arbitrage free market. Hence the Fundamental Theorem of Asset Pricing is extended so that it can apply for models with infinitely many assets. Mathematics Subject Classification (2000). 91B28, 28C15, 28A53.

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“…A recent projective system approach to the martingale characterization of the absence of arbitrage is provided by Balbás et al (2002). The equivalence between the absence of arbitrage and the existence of an equivalent martingale measure fails when an infinite number of trading dates is considered.…”

Section: The Fundamental Theorem Of Asset Pricingmentioning

confidence: 99%

An Overview of Probabilistic and Time Series Models in Finance

Balbás

Romera

Ruiz

Recent Advances in Applied Probability

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In this paper, we partially review probabilistic and time series models in finance. Both discrete and continuous-time models are described. The characterization of the No-Arbitrage paradigm is extensively studied in several financial market contexts. As the probabilistic models become more and more complex to be realistic, the Econometrics needed to estimate them are more difficult. Consequently, there is still much research to be done on the link between probabilistic and time series models.

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Projective system approach to the martingale characterization of the absence of arbitrage

Cited by 8 publications

References 17 publications

Pricing functionals and pricing measures

Pricing functionals and pricing measures

Infinitely Many Securities and the Fundamental Theorem of Asset Pricing

An Overview of Probabilistic and Time Series Models in Finance

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