The Role of Hellinger Processes in Mathematical Finance

The Role of Hellinger Processes in Mathematical Finance

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 wit...

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Bibliographic Details
Main Authors: T. R. Hurd, T. Choulli
Format: Article
Language:English
Published: MDPI AG 2001-09-01
Series:Entropy
Subjects:
information theory
Hellinger processes
optimal portfolios
Levy processes
financial mathematics
Online Access:http://www.mdpi.com/1099-4300/3/3/150/
Description
Summary: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.
ISSN:1099-4300

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