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Financial inverse problem and reconstruction of infinitely divisible distributions with Gaussian component

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Abstract

We consider an inverse problem of partial integro-differential equations of market prices of call options with many maturities and strike prices for geometric Lévy processes. We show the well-posedness (reconstruction, uniqueness, and stability) of the inverse problem among the class of infinitely divisible distributions with analyticity.

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Authors and Affiliations

  1. Faculty of Culture and Information Science, Doshisha University, 1-3 Tatara Miyakodani, Kyotanabe City, Kyoto, 610-0394, Japan

    S. Kaji

  2. Department of Mathematics, Kwanseigakuin University, Gakuen 2-1, Sanda, 669-1337, Japan

    S. Kotani

Authors
  1. S. Kaji
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  2. S. Kotani
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Correspondence to S. Kaji.

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Kaji, S., Kotani, S. Financial inverse problem and reconstruction of infinitely divisible distributions with Gaussian component. Finance Stoch 16, 45–62 (2012). https://doi.org/10.1007/s00780-010-0138-4

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  • DOI: https://doi.org/10.1007/s00780-010-0138-4

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