The Harrison-Pliska arbitrage pricing theorem under transaction costs

@article{Kabanov2001TheHA,
  title={The Harrison-Pliska arbitrage pricing theorem under transaction costs},
  author={Yuri Kabanov and Ch. Stricker},
  journal={Journal of Mathematical Economics},
  year={2001},
  volume={35},
  pages={185-196}
}
Abstract We consider a simple multi-asset discrete-time model of a currency market with transaction costs assuming the finite number of states of the nature. Defining two kinds of arbitrage opportunities we study necessary and sufficient conditions for the absence of arbitrage. Our main result is a natural extension of the Harrison–Pliska theorem on asset pricing. We prove also a hedging theorem without supplementary hypotheses. 
No-arbitrage criteria for financial markets with efficient friction
TLDR
A hedging theorem is established giving a description of the set of initial endowments which allows to super-replicate a given contingent claim and is an extension of the Dalang–Morton–Willinger theorem. Expand
Fundamental Theorem of Asset Pricing under fixed and proportional transaction costs
We show that the absence of arbitrage in a model with both fixed and proportional transaction costs is equivalent to the existence of a family of absolutely continuous single-step probabilityExpand
Arbitrage and Hedging in Model-Independent Markets with Frictions
  • M. Burzoni
  • Economics, Computer Science
  • SIAM J. Financial Math.
  • 2016
TLDR
A probability-free version of the Robust No Arbitrage condition introduced in Schachermayer ['04] is considered and it is shown that this is equivalent to the existence of Consistent Price Systems. Expand
Robust No Arbitrage Condition for Continuous-time Models with Transaction Costs
AbstractWe extend the Robust No Free Lunch (RNFL) theorem formulated for discrete-time models with proportional transaction costs to general continuous-time settings. We prove that the (RNFL)Expand
Robust No Arbitrage Condition for Continuous-Time Models with Transaction Costs
We extend the Robust No Free Lunch (RNFL) theorem formulated for discrete-time models with proportional transaction costs to general continuous-time settings. We prove that the (RNFL) condition isExpand
No‐Arbitrage Pricing for Dividend‐Paying Securities in Discrete‐Time Markets with Transaction Costs
We prove a version of First Fundamental Theorem of Asset Pricing under transaction costs for discrete-time markets with dividend-paying securities. Specifically, we show that the no-arbitrageExpand
Arbitrage Under Transaction Costs Revisited
We present a novel arbitrage-related notion for markets with transaction costs in discrete time and characterize it in terms of price systems. Pertinence of this concept is demonstrated. A discussionExpand
General Arbitrage Pricing Model: II – Transaction Costs
In particular, it is proved that a dynamic model with an infinite number of assets satisfies the No Generalized Arbitrage condition (this notion was introduced in [2]) if and only if there exist anExpand
The Fundamental Theorem of Asset Pricing Under Transaction Costs
This paper proves the Fundamental Theorem of Asset Pricing with transaction costs, when bid and ask prices follow locally bounded cadlag (right-continuous, left-limited) processes. The Robust No FreeExpand
The fundamental theorem of asset pricing under transaction costs
This paper proves the fundamental theorem of asset pricing with transaction costs, when bid and ask prices follow locally bounded càdlàg (right-continuous, left-limited) processes.The robust no freeExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 15 REFERENCES
Hedging Under Transaction Costs in Currency Markets: A Continuous-Time Model
We consider a general semimartingale model of a currency market with transaction costs. Assuming that the price process is continuous and the solvency cone is proper we prove a hedging theoremExpand
Hedging and liquidation under transaction costs in currency markets
  • Y. Kabanov
  • Economics, Computer Science
  • Finance Stochastics
  • 1999
TLDR
A general semimartingale model of a currency market with transaction costs is considered and a description of the initial endowments which allow to hedge a contingent claim in various currencies by a self-financing portfolio is given. Expand
Martingales and Arbitrage in Securities Markets with Transaction Costs
Abstract We derive the implications from the absence of arbitrage in dynamic securities markets with bid-ask spreads. The absence of arbitrage is equivalent to the existence of at least an equivalentExpand
Hedging under Transaction Costs in Currency Markets: a Discrete-Time Model
We consider a discrete‐time model of a currency market with transaction costs and give a description of initial endowments that allow the investor to hedge a contingent claim in various currencies byExpand
No-Arbitrage and Equivalent Martingale Measures: An Elementary Proof of the Harrison–Pliska Theorem
We give a new proof of a key result to the theorem that in the discrete-time stochastic model of a frictionless security market the absence of arbitrage possibilities is equivalent to the existence...
Local martingales and the fundamental asset pricing theorems in the discrete-time case
Abstract. This paper is devoted to giving simpler proofs of the two fundamental theorems of asset pricing theory, in iscrete-time and finite horizon: namely the no-arbitrage theorem, and the marketExpand
Equivalent martingale measures and no-arbitrage
We give here an elementary proof of the fundamental theorem of discrete-time asset pricing, due originally to Dalang, Morton and Willinger. The essence is a simple utility-maximisation argument, andExpand
Martingales and stochastic integrals in the theory of continuous trading
This paper develops a general stochastic model of a frictionless security market with continuous trading. The vector price process is given by a semimartingale of a certain class, and the generalExpand
Equivalent martingale measures and no-arbitrage in stochastic securities market models
We characterize those vector-valued stochastic processes (with a finite index set and defined on an arbitrarystochasic base) which can become a martingale under an equivalent change of measure.ThisExpand
A Hilbert space proof of the fundamental theorem of asset pricing in finite discrete time
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 absenceExpand
...
1
2
...