The no-arbitrage property is widely accepted to be a centerpiece of modern financial mathematics and could be considered to be a financial law applicable to a large class of(idealized) markets.This paper addresses the...The no-arbitrage property is widely accepted to be a centerpiece of modern financial mathematics and could be considered to be a financial law applicable to a large class of(idealized) markets.This paper addresses the following basic question:can one characterize the class of transformations that leave the law of no-arbitrage invariant?We provide a geometric formalization of this question in a non probabilistic setting of discrete time-the so-called trajectorial models.The paper then characterizes,in a local sense,the no-arbitrage symmetries and illustrates their meaning with a detailed example.Our context makes the result available to the stochastic setting as a special case.展开更多
The present paper continues the topic of our recent paper in the same journal,aiming to show the role of structural stability in financial modeling.In the context of financial market modeling,structural stability mean...The present paper continues the topic of our recent paper in the same journal,aiming to show the role of structural stability in financial modeling.In the context of financial market modeling,structural stability means that a specific“no-arbitrage”property is unaffected by small(with respect to the Pompeiu–Hausdorff metric)perturbations of the model’s dynamics.We formulate,based on our economic interpretation,a new requirement concerning“no arbitrage”properties,which we call the“uncertainty principle”.This principle in the case of no-trading constraints is equivalent to structural stability.We demonstrate that structural stability is essential for a correct model approximation(which is used in our numerical method for superhedging price computation).We also show that structural stability is important for the continuity of superhedging prices and discuss the sufficient conditions for this continuity.展开更多
基金supported in part by an NSERC grantsupported in part by the National University of Mar del Plata,Argentina EXA902/18。
文摘The no-arbitrage property is widely accepted to be a centerpiece of modern financial mathematics and could be considered to be a financial law applicable to a large class of(idealized) markets.This paper addresses the following basic question:can one characterize the class of transformations that leave the law of no-arbitrage invariant?We provide a geometric formalization of this question in a non probabilistic setting of discrete time-the so-called trajectorial models.The paper then characterizes,in a local sense,the no-arbitrage symmetries and illustrates their meaning with a detailed example.Our context makes the result available to the stochastic setting as a special case.
文摘The present paper continues the topic of our recent paper in the same journal,aiming to show the role of structural stability in financial modeling.In the context of financial market modeling,structural stability means that a specific“no-arbitrage”property is unaffected by small(with respect to the Pompeiu–Hausdorff metric)perturbations of the model’s dynamics.We formulate,based on our economic interpretation,a new requirement concerning“no arbitrage”properties,which we call the“uncertainty principle”.This principle in the case of no-trading constraints is equivalent to structural stability.We demonstrate that structural stability is essential for a correct model approximation(which is used in our numerical method for superhedging price computation).We also show that structural stability is important for the continuity of superhedging prices and discuss the sufficient conditions for this continuity.
