The fundamental theorem of asset pricing for continuous processes under small transaction costs

Guasoni, Paolo; Rásonyi, Miklós; Schachermayer, Walter

doi:10.1007/s10436-008-0110-x

Cited by 98 publications

(154 citation statements)

References 25 publications

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“…This assumption is intimately related to the absence of arbitrage in continuous time financial markets with proportional transaction costs (see also [16,13] …”

Section: Assets and Trading Strategiesmentioning

confidence: 99%

Efficient portfolios in financial markets with proportional transaction costs

2013

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In this article, we characterize efficient portfolios, i.e. portfolios which are optimal for at least one rational agent, in a very general financial market model with proportional transaction costs. In our setting, transaction costs may be random, time-dependent, have jumps and the preferences of the agents are modeled by multivariate expected utility functions. Thanks to the dual formulation of expected multivariate utility maximization problem established in Campi and Owen [3], we provide a complete characterization of efficient portfolios, generalizing earlier results of Dybvig [10] and Jouini and Kallal [16]. We basically show that a portfolio is efficient if and only if it is cyclically anticomonotonic with respect to at least one consistent price system. Finally, we introduce the notion of utility price of a given contingent claim as the minimal amount of a given initial portfolio allowing any agent to reach the claim by trading in the market, and give a dual representation of it.

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“…This assumption is intimately related to the absence of arbitrage in continuous time financial markets with proportional transaction costs (see also [16,13] …”

Section: Assets and Trading Strategiesmentioning

confidence: 99%

Efficient portfolios in financial markets with proportional transaction costs

2013

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“…It is well known that the fractional Black-Scholes model in (2.1) is not free of arbitrage, [2,4,20,21]. One can find though a solution around this problem by either regularizing the paths of the fractional Brownian motion (see [3,20]), or by introducing transactions costs in the model (see [11]). By the former it is meant the construction of a family of stochastic processes which are similar to the fractional Brownian motion but carry a unique equivalent martingale measure.…”

Section: Fractional Binary Marketsmentioning

confidence: 99%

“…Since the fractional Brownian motion fails to be a semimartingale (see [4,18,20,21]), this model allows for a free lunch with vanishing risk (see [10]). This problem can be solved by either regularizing the paths of the fractional Brownian motion (see [3]), or by introducing transactions costs in the model (see [11]). …”

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confidence: 99%

Strong asymptotic arbitrage in the large fractional binary market

Cordero

Perez-Ostafe

2015

Math Finan Econ

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We study, from the perspective of large financial markets, the asymptotic arbitrage (AA) opportunities in a sequence of binary markets approximating the fractional Black-Scholes model. This approximating sequence was introduced by Sottinen and named fractional binary market. The large financial market under consideration does not satisfy the standard assumptions of the theory of AA. For this reason, we follow a constructive approach to show first that a strong AA (SAA) exists in the frictionless case. Indeed, with the help of an appropriate version of the law of large numbers and a stopping time procedure, we construct a sequence of self-financing trading strategies leading to the desired result. Next, we introduce, in each small market, proportional transaction costs, and we show that a slight modification of the previous trading strategies leads to a SAA when the transaction costs converge fast enough to 0.

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“…For each market n this condition is equivalent to the absence of arbitrage with arbitrarily small transaction costs λ > 0 on each market n, see [8] (we state the theorem in the appendix, Theorem 7.1).…”

Section: Large Financial Markets With Proportional Transaction Costsmentioning

confidence: 99%