Note: [2] Acknowledgements: The author is grateful to comments made to this paper by Prof. Phil Maymin (Polytechnic Institute of New York University), Prof. Raphael Douady (CNRS and University of Paris 1, Department of Economics, France), Prof. Dominique Guégan (CNRS and University of Paris 1, Department of Economics, France), Prof. Yaffa Machnes (Bar-Ilan University, Graduate School of Business and Administration, Israel), Prof. Gila Fruchter (Bar-Ilan University, Graduate School of Business and Administration, Israel), Prof. Jeremy Schiff (Bar-Ilan University, Department of Mathematics, Israel), Dr. Shlomit Zuta (Tel Aviv-Yaffo Academic College) and Prof. Tamir Agmon (Tel Aviv-Yaffo Academic College).
Abstract: This paper provides a “non-extensive” information theoretic perspective on the relationship between risk and incomplete states uncertainty. Theoretically and empirically, we demonstrate that a substitution effect between the latter two may take place. Theoretically, the “non-extensive” volatility measure is concave with respect to the standard (based on normal distribution) volatility measure. With the degree of concavity depending on an incomplete states uncertainty parameter-the Tsallis-q. Empirically, the latter negatively causes the normal measure of volatility, positively affecting the tails of the distribution of realised log-returns.
