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

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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

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    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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