Arbitrage theory in models with transaction costs beyond efficient friction

  • 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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Author:Alexander Molitor
Place of publication:Frankfurt am Main
Referee:Christoph Kühn, Christoph Czichowsky, Miklós Rásonyi
Document Type:Doctoral Thesis
Date of Publication (online):2022/03/30
Year of first Publication:2021
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Granting Institution:Johann Wolfgang Goethe-Universität
Date of final exam:2022/03/14
Release Date:2022/03/30
Tag:fundamental theorem of asset pricing; no unbounded profit with bounded risk; proportional transaction costs; semimartingales; stochastic integration
Page Number:114
Last Page:110
Institutes:Informatik und Mathematik
Dewey Decimal Classification:3 Sozialwissenschaften / 33 Wirtschaft / 330 Wirtschaft
5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoDeutsches Urheberrecht