In this paper a real analysis approach to stock price modelling is considered. A stock price and its return are defined in a duality to each other provided there exist suitable limits along a sequence of nested partitions of a time interval, mimicking sum and product integrals. It extends the...

We consider the maximization of the long-term growth rate in the Black–Scholes model under proportional transaction costs as in Taksar et al. (Math. Oper. Res. 13:277–294, <CitationRef CitationID="CR24">1988</CitationRef>). Similarly as in Kallsen and Muhle-Karbe (Ann. Appl. Probab. 20:1341–1358, <CitationRef CitationID="CR14">2010</CitationRef>) for optimal consumption over...</citationref></citationref>

<Para ID="Par1">We price a contingent claim liability (claim for short) using a utility indifference argument. We consider an agent with exponential utility, who invests in a stock and a money market account with the goal of maximizing the utility of his investment at the final time T in the presence of a...</para>

<Para ID="Par1">We give characterizations of asymptotic arbitrage of the first and second kind and of strong asymptotic arbitrage for a sequence of financial markets with small proportional transaction costs λ <Subscript> n </Subscript> on market n, in terms of contiguity properties of sequences of equivalent probability measures...</subscript></para>

To any utility maximization problem under transaction costs one can assign a frictionless model with a price process S <Superscript>∗</Superscript>, lying in the bid/ask price interval <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$[\underline{S}, \overline{S}]$</EquationSource> </InlineEquation>. Such a process S <Superscript>∗</Superscript> is called a shadow price if it provides the same optimal utility value as in the...</superscript></equationsource></inlineequation></superscript>

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 free lunch with vanishing risk condition (RNFLVR) for simple strategies is equivalent to the...

A duality for robust hedging with proportional transaction costs of path-dependent European options is obtained in a discrete-time financial market with one risky asset. The investor’s portfolio consists of a dynamically traded stock and a static position in vanilla options, which can be...

For utility maximization problems under proportional transaction costs, it has been observed that the original market with transaction costs can sometimes be replaced by a frictionless shadow market that yields the same optimal strategy and utility. However, the question of whether or not this...