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Cited by 220 publications
(361 citation statements)
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“…[9], [10], [17] and [31]). We will say that an (admissible self-financing) portfolio realizes arbitrage on the time interval [0, T * ] if for its value process V the following conditions are satisfied:…”
Section: Portfolios and Arbitragementioning
confidence: 99%
See 1 more Smart Citation
“…[9], [10], [17] and [31]). We will say that an (admissible self-financing) portfolio realizes arbitrage on the time interval [0, T * ] if for its value process V the following conditions are satisfied:…”
Section: Portfolios and Arbitragementioning
confidence: 99%
“…Shiryaev [26; Chapter VII, Section 2c] (see also Dasgupta and Kallianpur [7]) presented an explicit (self-financing) portfolio realizing an arbitrage opportunity by means of the pathwise stochastic integration (cf. Föllmer [9], Föllmer, Protter and Shiryaev [10], Lin [17] and Zähle [31]). The question of the existence of arbitrage in models with fractional Brownian motion was also studied in Salopek [24], Norvaiša [22], Sottinen [27] and Cheridito [4].…”
Section: Introductionmentioning
confidence: 99%
“…, B Hm and W , resp. Moreover, the method of showing convergence in probability of the Riemann-Stieltjes sums for the first integral in the above equation by means of the Taylor expansion is well-known from the literature and goes back to Föllmer [5]. In contrast to other papers we derive this convergence from that of the remaining integrals.…”
Section: Dx(t) = a 0 X(t) T Dw (T) + M J=1 A J X(t) T Db Hj (T) + Bmentioning
confidence: 79%
“…These formulas are related to the Itô formula which plays an important role in the stochastic calculus based on the stochastic integral with respect to a semimartingale. Several modifications of the stochastic integral have been developed which allow integration with respect to sample functions of continuous stochastic processes with zero quadratic variation (Föllmer [10]), or with respect to sample functions of a fractional Brownian motion B H with the Hurst exponent H ∈ (1/2, 1) (Ciesielski, Kerkyacharian and Roynette [3], Zähle [43]). We notice that the results of the present paper apply to sample functions of B H when the Hurst exponent H ∈ (1/3, 1), which includes the case of a Brownian motion: H = 1/2.…”
Section: 2mentioning
confidence: 99%