Mixed Brownian–fractional Brownian model: absence of arbitrage and related topics
- 1 October 2006
- journal article
- research article
- Published by Taylor & Francis Ltd in Stochastics
- Vol. 78 (5), 281-300
- https://doi.org/10.1080/17442500600859317
Abstract
We consider a mixed Brownian–fractional-Brownian model of a financial market. The class of self-financing strategies is restricted to Markov-type smooth functions. It is proved that such strategies satisfy a parabolic equation that can be reduced to heat equation. Then it is proved that the mixed model is arbitrage-free. Finally, the capital of the model is presented as the limit of a sequence of semimartingales.Keywords
This publication has 15 references indexed in Scilit:
- A note on Wick products and the fractional Black-Scholes modelFinance and Stochastics, 2005
- An S-transform approach to integration with respect to a fractional Brownian motionBernoulli, 2003
- A General Fractional White Noise Theory And Applications To FinanceMathematical Finance, 2003
- Mixed Fractional Brownian MotionBernoulli, 2001
- Integration with respect to Fractal Functions and Stochastic Calculus IIMathematische Nachrichten, 2001
- The absence of arbitrage in a model with fractal Brownian motionRussian Mathematical Surveys, 1999
- An Elementary Approach to a Girsanov Formula and Other Analytical Results on Fractional Brownian MotionsBernoulli, 1999
- Integration with respect to fractal functions and stochastic calculus. IProbability Theory and Related Fields, 1998
- Arbitrage with Fractional Brownian MotionMathematical Finance, 1997
- Calcul d'ito sans probabilitesPublished by Springer Science and Business Media LLC ,1981