Functional equations for the stochastic exponential

Author:

Chikvinidze Besik12,Mania Michael13,Tevzadze Revaz12

Affiliation:

1. Business School, Georgian-American University, 8 Aleksidze Street, Tbilisi 0193, Georgia

2. Department of Stochastic Analysis and Mathematical Modeling, Institute of Cybernetics of Georgian Technical University, 5 Anjaparidze Street, Tbilisi 0186, Georgia

3. Department of Probability Theory and Mathematical Statistic, Razmadze Mathematical Institute of Tbilisi State University, 2 Aleksidze Street, Tbilisi 0193, Georgia

Abstract

In this paper, we consider two versions of functional equations for the stochastic exponential. One equation for a function of a semimartingale and its square characteristic and the second for non-anticipative functionals. A martingale characterization of the general solutions of these equations is given.

Publisher

World Scientific Pub Co Pte Ltd

Subject

Modeling and Simulation

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