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The Role of Hellinger Processes in Mathematical Finance
Mathematical Sciences Dept.; University of Alberta; Edmonton, Canada
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
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
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Choulli, T.; Hurd, T.R. The Role of Hellinger Processes in Mathematical Finance. Entropy 2001, 3, 150-161.
Choulli T, Hurd TR. The Role of Hellinger Processes in Mathematical Finance. Entropy. 2001; 3(3):150-161.
Choulli, T.; Hurd, T. R. 2001. "The Role of Hellinger Processes in Mathematical Finance." Entropy 3, no. 3: 150-161.