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

Deformed Exponentials and Applications to Finance

Dipartimento di Scienze Matematiche "G.L. Lagrange", Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
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 (CC BY 3.0).

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

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