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Entropy 2013, 15(9), 3471-3489; doi:10.3390/e15093471
Article

Deformed Exponentials and Applications to Finance

Received: 29 July 2013 / Revised: 22 August 2013 / Accepted: 26 August 2013 / Published: 2 September 2013
(This article belongs to the collection Advances in Applied Statistical Mechanics)
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Abstract

We illustrate some financial applications of the Tsallis and Kaniadakis deformed exponential. The minimization of the corresponding deformed divergence is discussed as a criterion to select a pricing measure in the valuation problems of incomplete markets. Moreover, heavy-tailed models for price processes are proposed, which generalized the well-known Black and Scholes model.
Keywords: deformed logarithm; deformed exponential; generalized entropy; martingale measure; generalized Fokker-Plank equation; non-Gaussian option pricing deformed logarithm; deformed exponential; generalized entropy; martingale measure; generalized Fokker-Plank equation; non-Gaussian option pricing
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Trivellato, B. Deformed Exponentials and Applications to Finance. Entropy 2013, 15, 3471-3489.

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