Fundamental Theorem of Asset Pricing under fixed and proportional transaction costs

@article{Brown2019FundamentalTO,
  title={Fundamental Theorem of Asset Pricing under fixed and proportional transaction costs},
  author={Martin Brown and T. Zastawniak},
  journal={Annals of Finance},
  year={2019},
  volume={16},
  pages={423-433}
}
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 probability measures, together with an adapted process with values within the bid-ask intervals that satisfies the martingale property with respect to each of the measures. This extends Harrison and Pliska’s classical Fundamental Theorem of Asset Pricing to the case of combined fixed and proportional transaction costs… Expand

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References

SHOWING 1-10 OF 29 REFERENCES
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
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 Harrison-Pliska arbitrage pricing theorem under transaction costs
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 arbitrageExpand
The fundamental theorem of asset pricing in the presence of bid-ask and interest rate spreads
Abstract We establish the fundamental theorem of asset pricing to a model with proportional transaction costs on trading in shares and different interest rates for borrowing and lending of cash. WeExpand
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
Dynamic Arbitrage-Free Asset Pricing with Proportional Transaction Costs
This paper studies multiperiod asset pricing theory in arbitrage-free financial markets with proportional transaction costs. The mathematical formulation is based on a Euclidean space for weaklyExpand
Arbitrage and Viability in Securities Markets with Fixed Trading Costs
This paper studies foundational issues in securities markets models with fixed costs of trading, i.e. transactions costs that are bounded regardless of the transaction size, such as fixed brokerageExpand
No Arbitrage Under Transaction Costs, with Fractional Brownian Motion and Beyond
We establish a simple no-arbitrage criterion that reduces the absence of arbitrage opportunities under proportional transaction costs to the condition that the asset price process may moveExpand
Martingales and Arbitrage in Securities Markets with Transaction Costs
We derive the implications from the absence of arbitrage in dynamic securities market with bi-ask spreads. The absence of arbitrage is equivalent to the existence of at least an equivalentExpand
Robust hedging with proportional transaction costs
TLDR
The main theorem is a duality between hedging and a Monge–Kantorovich-type optimization problem, where the optimization is over all probability measures that satisfy an approximate martingale condition related to consistent price systems. Expand
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