Entropy (Sep 2001)

The Role of Hellinger Processes in Mathematical Finance

  • T. R. Hurd,
  • T. Choulli

DOI
https://doi.org/10.3390/e3030150
Journal volume & issue
Vol. 3, no. 3
pp. 150 – 161

Abstract

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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