In this work we determine the financial laws according to which the risk-less component of a risky portfolio must evolve in order to avoid possibility of arbitrages when the dynamics of the stochastic component of the same portfolio is driven by a fractional Brownian motion. In order to deal with this problem, we specify a deterministic fractional differential equation and we solve it by using the Liouville's second method.
Fractional differo-integral calculus: Towards a theory of fractal financial laws
CORAZZA, Marco
;
2003-01-01
Abstract
In this work we determine the financial laws according to which the risk-less component of a risky portfolio must evolve in order to avoid possibility of arbitrages when the dynamics of the stochastic component of the same portfolio is driven by a fractional Brownian motion. In order to deal with this problem, we specify a deterministic fractional differential equation and we solve it by using the Liouville's second method.
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