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/
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spelling doaj-f334b8de6d53465da5f1f7fd7579dbbd2020-11-24T22:44:24ZengMDPI AGEntropy1099-43002001-09-013315016110.3390/e3030150The Role of Hellinger Processes in Mathematical FinanceT. R. HurdT. ChoulliThis 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.http://www.mdpi.com/1099-4300/3/3/150/information theoryHellinger processesoptimal portfoliosLevy processesfinancial mathematics
collection DOAJ
language English
format Article
sources DOAJ
author T. R. Hurd
T. Choulli
spellingShingle T. R. Hurd
T. Choulli
The Role of Hellinger Processes in Mathematical Finance
Entropy
information theory
Hellinger processes
optimal portfolios
Levy processes
financial mathematics
author_facet T. R. Hurd
T. Choulli
author_sort T. R. Hurd
title The Role of Hellinger Processes in Mathematical Finance
title_short The Role of Hellinger Processes in Mathematical Finance
title_full The Role of Hellinger Processes in Mathematical Finance
title_fullStr The Role of Hellinger Processes in Mathematical Finance
title_full_unstemmed The Role of Hellinger Processes in Mathematical Finance
title_sort role of hellinger processes in mathematical finance
publisher MDPI AG
series Entropy
issn 1099-4300
publishDate 2001-09-01
description 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.
topic information theory
Hellinger processes
optimal portfolios
Levy processes
financial mathematics
url http://www.mdpi.com/1099-4300/3/3/150/
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AT tchoulli theroleofhellingerprocessesinmathematicalfinance
AT trhurd roleofhellingerprocessesinmathematicalfinance
AT tchoulli roleofhellingerprocessesinmathematicalfinance
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