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

Kühn, Christoph; Molitor, Alexander

doi:10.1007/s00780-019-00403-5

Cited by 5 publications

(2 citation statements)

References 39 publications

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“…This changed with the rapid developments in program trading (whether implemented at low or high frequency) and the emergence of the notion of price impact which is now modelled and studied at the level of the order books. See also the paper [51] published in Finance and Stochastics. -The search for arbitrage-free models led naturally to the introduction of market models intended to reconcile stochastic models for the dynamics of derivative prices with models of the time evolutions of the underlying instruments.…”

Section: Introductionmentioning

confidence: 99%

The influence of economic research on financial mathematics: Evidence from the last 25 years

Carmona

2021

Finance Stoch

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Section: Introductionmentioning

confidence: 99%

The influence of economic research on financial mathematics: Evidence from the last 25 years

Carmona

2021

Finance Stoch

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“…Chapter 2 corresponds to the article Kühn and Molitor [66]. The new prospective strict-no arbitrage condition is introduced in Section 2.2.…”

Section: Overview Of the Thesismentioning

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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On the quasi-sure superhedging duality with frictions

Bayraktar

Burzoni

2019

Finance Stoch

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We prove the superhedging duality for a discrete-time financial market with proportional transaction costs under model uncertainty. Frictions are modeled through solvency cones as in the original model of Kabanov [1999] adapted to the quasi-sure setup of Bouchard and Nutz [2015]. Our approach allows to remove the restrictive assumption of No Arbitrage of the Second Kind considered in Bouchard et al. [2017] and to show the duality under the more natural condition of No Strict Arbitrage. In addition, we extend the results to models with portfolio constraints.

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

Cited by 5 publications

References 39 publications

The influence of economic research on financial mathematics: Evidence from the last 25 years

The influence of economic research on financial mathematics: Evidence from the last 25 years

Arbitrage theory in models with transaction costs beyond efficient friction

On the quasi-sure superhedging duality with frictions

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