Smearing Distributions and their use in Financial Markets

Abstract

It is shown that superpositions of path integrals with arbitrary Hamiltonians and different scaling parameters v ("variances") obey the Chapman-Kolmogorov relation for Markovian processes if and only if the corresponding smearing distributions for v have a specific functional form. Ensuing "smearing" distributions substantially simplify the coupled system of Fokker-Planck equations for smeared and un-smeared conditional probabilities. Simple application in financial models with stochastic volatility is presented.

6 pages. Presented at the International Conference: Path Integrals - New Trends and Perspectives, Dresden, Germany, September 23 - 28, 2007