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Old Problems, Classical Methods, New Solutions

Author

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  • ALEXANDER LIPTON

    (The Jerusalem School of Business Administration, The Hebrew University of Jerusalem, Jerusalem, Israel2Connection Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA3Sila, Portland, OR, USA)

Abstract

We use a powerful extension of the classical method of heat potentials, recently developed by the present author and his collaborators, to solve several significant problems of financial mathematics. We consider the following problems in detail: (a) calibrating the default boundary in the structural default framework to a constant default intensity; (b) calculating default probability for a representative bank in the mean-field framework; and (c) finding the hitting time probability density of an Ornstein–Uhlenbeck process. Several other problems, including pricing American put options and finding optimal mean-reverting trading strategies, are mentioned in passing. Besides, two nonfinancial applications — the supercooled Stefan problem and the integrate-and-fire neuroscience problem — are briefly discussed as well.

Suggested Citation

  • Alexander Lipton, 2020. "Old Problems, Classical Methods, New Solutions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(04), pages 1-37, June.
    • Handle: RePEc:wsi:ijtafx:v:23:y:2020:i:04:n:s0219024920500247
    DOI: 10.1142/S0219024920500247
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