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The fractional Black-Scholes equation. (English) Zbl 1058.91045
The Black-Scholes equation for the option of a European call involves the first derivative in time. Replacing this derivative by a fractional derivative of order $\alpha$, $0<\alpha<1$, leads to the fractional Black--Scholes equation. The author gives the complete solution to this equation with the help of Mellin, Laplace transformations and Green functions. He also finds the corresponding $\Delta(\alpha)$, the Delta of call option, $\Delta(\alpha)=\partial C(S,t)/\partial S$. Any information about $\Delta(\alpha)$ gives some information on the order $\alpha$.

91B28Finance etc. (MSC2000)
26A33Fractional derivatives and integrals (real functions)
62P05Applications of statistics to actuarial sciences and financial mathematics
33C60Hypergeometric integrals and functions defined by them