How local in time is the no-arbitrage property under capital gains taxes?

Kühn, Christoph

doi:10.1007/s11579-018-0230-7

Cited by 3 publications

(4 citation statements)

References 23 publications

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“…Their proof uses the existence of a CPS that is guaranteed by Grigoriev [Gri05] in the case of an arbitrage-free model with two assets. On the other hand, already for three assets, there is a counterexample showing that (NA) does not imply the existence of a CPS (see Example 4.6 in [Küh18]). The goal of the current paper is twofold:…”

Section: Introductionmentioning

confidence: 99%

“…This scheme can be formalized in a quite canonical way in diverse market models including, e.g., capital gains taxes, uncertainty about the execution of limit orders, or dividend paying assets, where the basic problem from Example 3.1 in Schachermayer [Sch04], can also occur (see, e.g., Example 4.5 in [Küh18]). The arguments of our proofs may be adapted to these models to show that the set of attainable terminal portfolios is closed.…”

Section: Introductionmentioning

confidence: 99%

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Prospective strict no-arbitrage and the fundamental theorem of asset pricing under transaction costs

Kühn

Molitor

2019

Finance Stoch

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In discrete time markets with proportional transaction costs, Schachermayer [Sch04] shows that robust no-arbitrage is equivalent to the existence of a strictly consistent price system.In this paper, we introduce the concept of prospective strict no-arbitrage that is a variant of the strict no-arbitrage property from Kabanov, Rásonyi, and Stricker [KRS02]. The prospective strict no-arbitrage condition is slightly weaker than robust no-arbitrage, and it implies that the set of portfolios attainable from zero initial endowment is closed in probability. A weak version of prospective strict no-arbitrage turns out to be equivalent to the existence of a consistent price system. In contrast to the fundamental theorem of asset pricing of Schachermayer [Sch04], the consistent frictionless prices may lie on the boundary of the bid-ask spread.On the technical level, a crucial difference to Schachermayer [Sch04] and Kabanov-Rásonyi-Stricker [KRS03] is that we prove closedness without having at hand that the nullstrategies form a linear space.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Prospective strict no-arbitrage and the fundamental theorem of asset pricing under transaction costs

Kühn

Molitor

2019

Finance Stoch

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“…In the case of only two assets, Grigoriev [34] shows that (NA) is equivalent to the existence of a CPS -although the set of hedgeable claims attainable from zero endowment need not be closed (see, e.g., [34,Example 1.3]). As already mentioned, this analogy of the frictionless FTAP fails in higher dimensions (see [65,Example 4.6] for a counterexample with three assets). This means that (NA ps ) cannot be equivalent to the existence of a CPS.…”

Section: The Discrete-time Casementioning

confidence: 95%

“…This scheme can be formalized in a quite canonical way in diverse market models including, e.g., capital gains taxes, uncertainty about the execution of limit orders, or dividend paying assets, where the basic problem from Example 3.1 in Schachermayer [85], can also occur (see, e.g., Example 4.5 in [65]). The arguments of our proofs may be adapted to these models to show that the set of attainable terminal portfolios is closed.…”

Section: Prospective Strict No-arbitrage and Consistent Price Systemsmentioning

confidence: 99%

Arbitrage theory in models with transaction costs beyond efficient friction

Molitor¹

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In the first part of this thesis, we introduce the concept of prospective strict no-arbitrage for discrete-time financial market models with proportional transaction. The prospective strict no-arbitrage condition, which is a variant of strict no-arbitrage, is slightly weaker than the robust no-arbitrage condition. It still implies that the set of portfolios attainable from zero initial endowment is closed in probability. Consequently, prospective strict no-arbitrage implies the existence of consistent prices, which may lie on the boundary of the bid-ask spread. A weak version of prospective strict no-arbitrage turns out to be equivalent to the existence of a consistent price system. In continuous-time financial market models with proportional transaction costs, efficient friction, i.e., nonvanishing transaction costs, is a standing assumption. Together with robust no free lunch with vanishing risk, it rules out strategies of infinite variation which usually appear in frictionless financial markets. In the second part of this thesis, we show how models with and without transaction costs can be unified. The bid and the ask price of a risky asset are given by cadlag processes which are locally bounded from below and may coincide at some points. In a first step, we show that if the bid-ask model satisfies no unbounded profit with bounded risk for simple long-only strategies, then there exists a semimartingale lying between the bid and the ask price process. In a second step, under the additional assumption that the zeros of the bid-ask spread are either starting points of an excursion away from zero or inner points from the right, we show that for every bounded predictable strategy specifying the amount of risky assets, the semimartingale can be used to construct the corresponding self-financing risk-free position in a consistent way. Finally, the set of most general strategies is introduced, which also provides a new view on the frictionless case.

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Arbitrage and non-linear taxes

Becker,

Löffler

2024

Rev Manag Sci

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Incorporating a progressive income tax into an economic decision problem raises the question whether this tax does not create arbitrage opportunities. We investigate this problem in a riskless (multi-period) economy. With a convex tax function we identify a particular kind of arbitrage (called bounded arbitrage): In this case the gain achievable through arbitrage trade is limited and cannot reach infinity.We are able to give a complete characterisation based on prizes of the traded assets as to whether bounded as well as unbounded arbitrage opportunities will exist.

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How local in time is the no-arbitrage property under capital gains taxes?

Cited by 3 publications

References 23 publications

Prospective strict no-arbitrage and the fundamental theorem of asset pricing under transaction costs

Prospective strict no-arbitrage and the fundamental theorem of asset pricing under transaction costs

Arbitrage theory in models with transaction costs beyond efficient friction

Arbitrage and non-linear taxes

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