T. Choulli ^1,* and T. R. Hurd ^2,§

¹ Mathematical Sciences Dept.; University of Alberta; Edmonton, Canada; T6G 2E9 E-mail: [email protected]
² Dept. of Mathematics and Statistics; McMaster University; Hamilton, Canada; L8S 4K1
E-mail: [email protected],
http://icarus.math.mcmaster.ca/tom/tom.html

^* This author gratefully acknowledges the financial support of MITACS and the hospitality and support of PhiMAC, the Mathematical Finance Lab at McMaster University, as the major part of this work was developed at McMaster University.
^§ Research supported by the Natural Sciences and Engineering Research Council of Canada and MITACS, Canada.

Received: 7 September 2001 / Accepted: 15 September 2001 / Published: 30 September 2001

Abstract: This paper illustrates the natural role that Hellinger processes can play in solving problems from finance. We propose an extension of the concept of Hellinger process applicable to entropy distance and f-divergence distances, where f is a convex logarithmic function or a convex power function with general order q, 0≠q<1. These concepts lead to a new approach to Merton's optimal portfolio problem and its dual in general Lévy markets.

Keywords: information theory; Hellinger processes; optimal portfolios; Levy processes; financial mathematics.