The fundamental theorem of asset pricing in the presence of bid-ask and interest rate spreads

@article{Roux2011TheFT,
  title={The fundamental theorem of asset pricing in the presence of bid-ask and interest rate spreads},
  author={Alet Roux},
  journal={Journal of Mathematical Economics},
  year={2011},
  volume={47},
  pages={159-163}
}
  • Alet Roux
  • Published 2011
  • Economics
  • Journal of Mathematical Economics
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. We show that such a model is free of arbitrage if and only if one can embed in it a friction-free model that is itself free of arbitrage, i.e. if there exists an artificial friction-free price for the stock between its bid and ask prices and an artificial interest rate between the borrowing and lending… 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
Asset pricing in an imperfect world
In a model with no given probability measure, we consider asset pricing in the presence of frictions and other imperfections and characterize the property of coherent pricing, a notion related toExpand
Stochastic Dynamics of Financial Markets
This thesis provides a study on stochastic models of financial markets related to problems of asset pricing and hedging, optimal portfolio managing and statistical changepoint detection in trends ofExpand
DEPARTMENT OF ECONOMICS, MANAGEMENT AND STATISTICS UNIVERSITY OF MILAN – BICOCCA
In a model with no given probability measure, we consider asset pricing in the presence of frictions and other imperfections and characterize the property of coherent pricing, a notion related toExpand
Good deal bounds with convex constraints
We investigate the structure of good deal bounds, which are subintervals of a no-arbitrage pricing bound, for financial market models with convex constraints as an extension of Arai and FukasawaExpand
A comparison of two no-arbitrage conditions
We give a comparison of two no-arbitrage conditions for the fundamental theorem of asset pricing. The first condition is named as the no free lunch with vanishing risk condition and the second the noExpand
Good deal bounds with convex constraints: --- examples and proofs ---
This note is an extended version of Arai (2016), in which convex risk measures describing the upper and lower bounds of a good deal bound are studied for the case where the set of 0-attainable claimsExpand
Option Pricing in an Imperfect World
In a model with no given probability measure, we consider asset pricing in the presence of frictions and other imperfections and characterize the property of coherent pricing, a notion related toExpand

References

SHOWING 1-10 OF 19 REFERENCES
The fundamental theorem of asset pricing with cone constraints
Abstract In frictionless securities markets, the characterization of the no arbitrage condition by the existence of equivalent martingale measures in discrete time is known as the fundamental TheoremExpand
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
The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time
We prove a version of the Fundamental Theorem of Asset Pricing, which applies to Kabanov's approach to foreign exchange markets under transaction costs. The financial market is modelled by a d x dExpand
ARBITRAGE IN SECURITIES MARKETS WITH SHORT-SALES CONSTRAINTS
In this paper we derive the implications of the absence of arbitrage in securities markets models where traded securities are subject to short-sales constraints and where the borrowing and lendingExpand
Asset Pricing and Hedging in Financial Markets with Transaction Costs: An Approach Based on the Von Neumann–Gale Model
The paper develops a general discrete-time framework for asset pricing and hedging in financial markets with proportional transaction costs and trading constraints. The framework is suggested byExpand
Arbitrage, linear programming and martingales¶in securities markets with bid-ask spreads
Abstract. In a general, finite-dimensional securities market model with bid-ask spreads, we characterize absence of arbitrage opportunities both by linear programming and in terms of martingales. 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
On the Fundamental Theorem of Asset Pricing: Random Constraints and Bang-Bang No-Arbitrage Criteria
The paper generalizes and refines the Fundamental Theorem of Asset Pricing of Dalang, Morton, and Willinger (1990) in the following two respects: (a) the result is extended to a model with generalExpand
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
...
1
2
...