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Entropy 2001, 3(3), 150-161; doi:10.3390/e3030150
Article

The Role of Hellinger Processes in Mathematical Finance

1
 and
2
1 Mathematical Sciences Dept.; University of Alberta; Edmonton, Canada 2 Dept. of Mathematics and Statistics; McMaster University; Hamilton, Canada
* Author to whom correspondence should be addressed.
Received: 7 September 2001 / Accepted: 15 September 2001 / Published: 30 September 2001
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Abstract

This paper illustrates the natural role that Hellinger processes can play in solving problems from ¯nance. 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 6= q < 1. These concepts lead to a new approach to Merton's optimal portfolio problem and its dual in general L¶evy markets.
Keywords: information theory; Hellinger processes; optimal portfolios; Levy processes; financial mathematics information theory; Hellinger processes; optimal portfolios; Levy processes; financial mathematics
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Choulli, T.; Hurd, T.R. The Role of Hellinger Processes in Mathematical Finance. Entropy 2001, 3, 150-161.

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