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Inverse problem and concentration method of a continuous-in-time financial model

Author

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  • Tarik Chakkour

    (Laboratory of Mathematics of Atlantic Brittany, University of Bretagne-Sud, UMR 6205, LMBA, F-56000 Vannes, France)

  • Emmanuel Frénod

    (Laboratory of Mathematics of Atlantic Brittany, University of Bretagne-Sud, UMR 6205, LMBA, F-56000 Vannes, France)

Abstract

In a continuous-in-time model, there is an important financial quantity called Loan which cannot be determined directly in terms of algebraic spending but has a major impact on the financial strategy. In this paper, we use a mathematical framework to discuss an inverse problem of determining the implied Loan Measure from Algebraic Spending Measure when it is possible. In addition, we build a numerical method to concentrate a measure as a sum of Dirac masses.

Suggested Citation

  • Tarik Chakkour & Emmanuel Frénod, 2016. "Inverse problem and concentration method of a continuous-in-time financial model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(02), pages 1-20, June.
    • Handle: RePEc:wsi:ijfexx:v:03:y:2016:i:02:n:s242478631650016x
    DOI: 10.1142/S242478631650016X
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    References listed on IDEAS

    as
    1. Merton, Robert C., 1975. "Theory of Finance from the Perspective of Continuous Time," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 10(4), pages 659-674, November.
    2. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    3. Carl Chiarella & Mark Craddock & Nadima El-Hassan, 2000. "The Calibration of Stock Option Pricing Models Using Inverse Problem Methodology," Research Paper Series 39, Quantitative Finance Research Centre, University of Technology, Sydney.
    4. Emmanuel Frenod & Tarik Chakkour, 2016. "A continuous-in-time financial model," Post-Print hal-01249324, HAL.
    5. Sundaresan, S.M., 2000. "Continuous-Time Methods in Finance: A Review and an Assessment," Papers 00-03, Columbia - Graduate School of Business.
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    Cited by:

    1. Tarik Chakkour, 2017. "Some Notes about the Continuous-in-Time Financial Model," Post-Print hal-01584982, HAL.

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