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Arbitrage in a discrete version of the Wick-Fractional Black Scholes model

Bender, C.; Elliott, R.
Fonte: Inst Operations Research Management Sciences Publicador: Inst Operations Research Management Sciences
Tipo: Artigo de Revista Científica
Publicado em //2004 Português
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We consider binary market models based on the discrete Wick product instead of the pathwise product and provide a sufficient criterion for the existence of an arbitrage. This arbitrage is explicitly constructed in the class of self-financing one-step buy-and-hold strategies, (i.e., the investor holds shares of the stock only at one time step). Using coefficients obtained from an approximation of a fractional Brownian motion with Hurst parameter ½ < H < 1 the result is applied to a discrete version of the (Wick-)fractional Black-Scholes market.; Christian Bender and Robert J. Elliott