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Information geometry of L\'evy processes and financial models

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  • Jaehyung Choi

Abstract

We explore the information geometry of L\'evy processes. As a starting point, we derive the $\alpha$-divergence between two L\'evy processes. Subsequently, the Fisher information matrix and the $\alpha$-connection associated with the geometry of L\'evy processes are computed from the $\alpha$-divergence. In addition, we discuss statistical applications of this information geometry. As illustrative examples, we investigate the differential-geometric structures of various L\'evy processes relevant to financial modeling, including tempered stable processes, the CGMY model, and variance gamma processes.

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  • Jaehyung Choi, 2025. "Information geometry of L\'evy processes and financial models," Papers 2507.23646, arXiv.org.
    • Handle: RePEc:arx:papers:2507.23646
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