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Bezirgen Veliyev - One of the best experts on this subject based on the ideXlab platform.

  • a direct proof of the bichteler dellacherie theorem and connections to arbitrage
    Annals of Probability, 2011
    Co-Authors: Mathias Beiglbock, Walter Schachermayer, Bezirgen Veliyev
    Abstract:

    We give an elementary proof of the celebrated Bichteler–Dellacherie theorem which states that the class of stochastic processes S allowing for a useful integration theory consists precisely of those processes which can be written in the form S = M + A, where M is a local martingale and A is a Finite Variation process. In other words, S is a good integrator if and only if it is a semi-martingale. We obtain this decomposition rather directly from an elementary discrete-time Doob–Meyer decomposition. By passing to convex combinations, we obtain a direct construction of the continuous time decomposition, which then yields the desired decomposition. As a by-product of our proof, we obtain a characterization of semi-martingales in terms of a variant of no free lunch, thus extending a result from [Math. Ann. 300 (1994) 463–520].

  • a direct proof of the bichteler dellacherie theorem and connections to arbitrage
    arXiv: Probability, 2010
    Co-Authors: Mathias Beiglbock, Walter Schachermayer, Bezirgen Veliyev
    Abstract:

    We give an elementary proof of the celebrated Bichteler-Dellacherie Theorem which states that the class of stochastic processes $S$ allowing for a useful integration theory consists precisely of those processes which can be written in the form $S=M+A$, where $M$ is a local martingale and $A$ is a Finite Variation process. In other words, $S$ is a good integrator if and only if it is a semi-martingale. We obtain this decomposition rather directly from an elementary discrete-time Doob-Meyer decomposition. By passing to convex combinations we obtain a direct construction of the continuous time decomposition, which then yields the desired decomposition. As a by-product of our proof we obtain a characterization of semi-martingales in terms of a variant of \emph{no free lunch}, thus extending a result from [DeSc94].

Walter Schachermayer - One of the best experts on this subject based on the ideXlab platform.

  • a direct proof of the bichteler dellacherie theorem and connections to arbitrage
    Annals of Probability, 2011
    Co-Authors: Mathias Beiglbock, Walter Schachermayer, Bezirgen Veliyev
    Abstract:

    We give an elementary proof of the celebrated Bichteler–Dellacherie theorem which states that the class of stochastic processes S allowing for a useful integration theory consists precisely of those processes which can be written in the form S = M + A, where M is a local martingale and A is a Finite Variation process. In other words, S is a good integrator if and only if it is a semi-martingale. We obtain this decomposition rather directly from an elementary discrete-time Doob–Meyer decomposition. By passing to convex combinations, we obtain a direct construction of the continuous time decomposition, which then yields the desired decomposition. As a by-product of our proof, we obtain a characterization of semi-martingales in terms of a variant of no free lunch, thus extending a result from [Math. Ann. 300 (1994) 463–520].

  • a direct proof of the bichteler dellacherie theorem and connections to arbitrage
    arXiv: Probability, 2010
    Co-Authors: Mathias Beiglbock, Walter Schachermayer, Bezirgen Veliyev
    Abstract:

    We give an elementary proof of the celebrated Bichteler-Dellacherie Theorem which states that the class of stochastic processes $S$ allowing for a useful integration theory consists precisely of those processes which can be written in the form $S=M+A$, where $M$ is a local martingale and $A$ is a Finite Variation process. In other words, $S$ is a good integrator if and only if it is a semi-martingale. We obtain this decomposition rather directly from an elementary discrete-time Doob-Meyer decomposition. By passing to convex combinations we obtain a direct construction of the continuous time decomposition, which then yields the desired decomposition. As a by-product of our proof we obtain a characterization of semi-martingales in terms of a variant of \emph{no free lunch}, thus extending a result from [DeSc94].

  • a super replication theorem in kabanov s model of transaction costs
    Economics Papers from University Paris Dauphine, 2006
    Co-Authors: Luciano Campi, Walter Schachermayer
    Abstract:

    We prove a general version of the super-replication theorem, which applies to Kabanov’s model of foreign exchange markets under proportional transaction costs. The market is described by a matrix-valued cadlag bid-ask process $$(\Pi_t)_{t\in [0,T]}$$ evolving in continuous time. We propose a new definition of admissible portfolio processes as predictable (not necessarily right- or left- continuous) processes of Finite Variation related to the bid-ask process by economically meaningful relations. Under the assumption of existence of a strictly consistent price system (SCPS), we prove a closedness property for the set of attainable vector-valued contingent claims. We then obtain the super-replication theorem as a consequence of that property, thus generalizing to possibly discontinuous bid-ask processes analogous results obtained by Kabanov (Financ. Stoch. 3, 237–248, 1999), Kabanov and Last (Math. Financ. 12, 63–70, 2002) and Kabanov and Stricker (Advances in Finance and Stochastics: Essays in Honour of Dieter Sondermann, pp 125–136, 2002). Rasonyi’s counter-example (Lecture Notes in Mathematics 1832, 394–398, 2003) served as an important motivation for our approach.

Mathias Beiglbock - One of the best experts on this subject based on the ideXlab platform.

  • a direct proof of the bichteler dellacherie theorem and connections to arbitrage
    Annals of Probability, 2011
    Co-Authors: Mathias Beiglbock, Walter Schachermayer, Bezirgen Veliyev
    Abstract:

    We give an elementary proof of the celebrated Bichteler–Dellacherie theorem which states that the class of stochastic processes S allowing for a useful integration theory consists precisely of those processes which can be written in the form S = M + A, where M is a local martingale and A is a Finite Variation process. In other words, S is a good integrator if and only if it is a semi-martingale. We obtain this decomposition rather directly from an elementary discrete-time Doob–Meyer decomposition. By passing to convex combinations, we obtain a direct construction of the continuous time decomposition, which then yields the desired decomposition. As a by-product of our proof, we obtain a characterization of semi-martingales in terms of a variant of no free lunch, thus extending a result from [Math. Ann. 300 (1994) 463–520].

  • a direct proof of the bichteler dellacherie theorem and connections to arbitrage
    arXiv: Probability, 2010
    Co-Authors: Mathias Beiglbock, Walter Schachermayer, Bezirgen Veliyev
    Abstract:

    We give an elementary proof of the celebrated Bichteler-Dellacherie Theorem which states that the class of stochastic processes $S$ allowing for a useful integration theory consists precisely of those processes which can be written in the form $S=M+A$, where $M$ is a local martingale and $A$ is a Finite Variation process. In other words, $S$ is a good integrator if and only if it is a semi-martingale. We obtain this decomposition rather directly from an elementary discrete-time Doob-Meyer decomposition. By passing to convex combinations we obtain a direct construction of the continuous time decomposition, which then yields the desired decomposition. As a by-product of our proof we obtain a characterization of semi-martingales in terms of a variant of \emph{no free lunch}, thus extending a result from [DeSc94].

Justin Yang - One of the best experts on this subject based on the ideXlab platform.

  • continuous time analysis of fleeting discrete price moves
    Journal of the American Statistical Association, 2017
    Co-Authors: Neil Shephard, Justin Yang
    Abstract:

    ABSTRACTThis article proposes a novel model of financial prices where (i) prices are discrete; (ii) prices change in continuous time; (iii) a high proportion of price changes are reversed in a fraction of a second. Our model is analytically tractable and directly formulated in terms of the calendar time and price impact curve. The resulting cadlag price process is a piecewise constant semimartingale with Finite activity, Finite Variation, and no Brownian motion component. We use moment-based estimations to fit four high-frequency futures datasets and demonstrate the descriptive power of our proposed model. This model is able to describe the observed dynamics of price changes over three different orders of magnitude of time intervals. Supplementary materials for this article are available online.

  • continuous time analysis of fleeting discrete price moves
    2014
    Co-Authors: Neil Shephard, Justin Yang
    Abstract:

    This paper proposes a novel model of financial prices where: (i) prices are discrete; (ii) prices change in continuous time; (iii) a high proportion of price changes are reversed in a fraction of a second. Our model is analytically tractable and the role of the calendar time can be explicitly understood. It is directly formulated in terms of the price impact curve. The resulting cadlag price process is a piecewise constant semimartingale with Finite activity, Finite Variation and no Brownian motion component. We use moment-based estimations to fit four high frequency futures data sets and demonstrate the descriptive power of our proposed model. This model is able to describe the observed dynamics of price changes over three different orders of magnitude of time intervals.

  • continuous time analysis of fleeting discrete price moves
    2014
    Co-Authors: Neil Shephard, Justin Yang
    Abstract:

    This paper proposes a novel model of financial prices where: (i) prices are discrete; (ii) prices change in continuous time; (iii) a high proportion of price changes are reversed in a fraction of a second. Our model is analytically tractable and directly formulated in terms of the calendar time and price impact curve. The resulting c\`{a}dl\`{a}g price process is a piecewise constant semimartingale with Finite activity, Finite Variation and no Brownian motion component. We use moment-based estimations to fit four high frequency futures data sets and demonstrate the descriptive power of our proposed model. This model is able to describe the observed dynamics of price changes over three different orders of magnitude of time intervals.

Neil Shephard - One of the best experts on this subject based on the ideXlab platform.

  • continuous time analysis of fleeting discrete price moves
    Journal of the American Statistical Association, 2017
    Co-Authors: Neil Shephard, Justin Yang
    Abstract:

    ABSTRACTThis article proposes a novel model of financial prices where (i) prices are discrete; (ii) prices change in continuous time; (iii) a high proportion of price changes are reversed in a fraction of a second. Our model is analytically tractable and directly formulated in terms of the calendar time and price impact curve. The resulting cadlag price process is a piecewise constant semimartingale with Finite activity, Finite Variation, and no Brownian motion component. We use moment-based estimations to fit four high-frequency futures datasets and demonstrate the descriptive power of our proposed model. This model is able to describe the observed dynamics of price changes over three different orders of magnitude of time intervals. Supplementary materials for this article are available online.

  • continuous time analysis of fleeting discrete price moves
    2014
    Co-Authors: Neil Shephard, Justin Yang
    Abstract:

    This paper proposes a novel model of financial prices where: (i) prices are discrete; (ii) prices change in continuous time; (iii) a high proportion of price changes are reversed in a fraction of a second. Our model is analytically tractable and the role of the calendar time can be explicitly understood. It is directly formulated in terms of the price impact curve. The resulting cadlag price process is a piecewise constant semimartingale with Finite activity, Finite Variation and no Brownian motion component. We use moment-based estimations to fit four high frequency futures data sets and demonstrate the descriptive power of our proposed model. This model is able to describe the observed dynamics of price changes over three different orders of magnitude of time intervals.

  • continuous time analysis of fleeting discrete price moves
    2014
    Co-Authors: Neil Shephard, Justin Yang
    Abstract:

    This paper proposes a novel model of financial prices where: (i) prices are discrete; (ii) prices change in continuous time; (iii) a high proportion of price changes are reversed in a fraction of a second. Our model is analytically tractable and directly formulated in terms of the calendar time and price impact curve. The resulting c\`{a}dl\`{a}g price process is a piecewise constant semimartingale with Finite activity, Finite Variation and no Brownian motion component. We use moment-based estimations to fit four high frequency futures data sets and demonstrate the descriptive power of our proposed model. This model is able to describe the observed dynamics of price changes over three different orders of magnitude of time intervals.