Scaling in financial prices: II. Multifractals and the star equation

Abstract

This is a direct continuation of the preceding paper, with which it shares the front material and the numbering of the sections. A little repetition makes it possible to read this paper, part II, by itself. It describes the progression of the formalism from the financial model the author introduced in 1963, with independence and [iopmath latex="$alphalt 2$"] <2 [/iopmath], to the financial model the author developed 1997, with multifractal dependence and [iopmath latex="$1lt alphalt infty$"] 1<< [/iopmath], and on to current developments. The long informal discussion in section 3 of the preceding paper is rephrased in formal fashion and extended. The presentation describes the original and the multifractal forms of a 'star equation' and then moves beyond it.