OLD PROBLEMS, CLASSICAL METHODS, NEW SOLUTIONS

Alexander Lipton
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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

International Journal of Theoretical and Applied Finance (IJTAF), 2020, vol. 23, issue 04, 1-37

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.

Keywords: Method of heat potentials; first hitting time density; Cherkasov condition; Volterra integral equation; Abel integral equation; Ornstein–Uhlenbeck process; pairs trading; structural default model; stability of banking system; Stefan problem; integrate-and-fire neuron excitation model (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S0219024920500247

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