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Generalized Integral Transforms in Mathematical Finance

Author

Listed:
  • Andrey Itkin

    (New York University, USA)

  • Alexander Lipton

    (Hebrew University of Jerusalem, Israel)

  • Dmitry Muravey

    (Moscow State University, Russia)

Abstract

This book describes several techniques, first invented in physics for solving problems of heat and mass transfer, and applies them to various problems of mathematical finance defined in domains with moving boundaries. These problems include: (a) semi-closed form pricing of options in the one-factor models with time-dependent barriers (Bachelier, Hull-White, CIR, CEV); (b) analyzing an interconnected banking system in the structural credit risk model with default contagion; (c) finding first hitting time density for a reducible diffusion process; (d) describing the exercise boundary of American options; (e) calculating default boundary for the structured default problem; (f) deriving a semi-closed form solution for optimal mean-reverting trading strategies; to mention but some.

Suggested Citation

  • Andrey Itkin & Alexander Lipton & Dmitry Muravey, 2021. "Generalized Integral Transforms in Mathematical Finance," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 12147, December.
    • Handle: RePEc:wsi:wsbook:12147
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    File URL: https://www.worldscientific.com/worldscibooks/10.1142/12147
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    Citations

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    Cited by:

    1. Andrey Itkin & Dmitry Muravey, 2021. "Semi-analytical pricing of barrier options in the time-dependent $\lambda$-SABR model," Papers 2109.02134, arXiv.org.
    2. Andrey Itkin, 2023. "Semi-analytic pricing of American options in time-dependent jump-diffusion models with exponential jumps," Papers 2308.08760, arXiv.org, revised Feb 2024.
    3. Itkin, Andrey & Lipton, Alexander & Muravey, Dmitry, 2022. "Multilayer heat equations and their solutions via oscillating integral transforms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 601(C).
    4. Alexander Lipton & Artur Sepp, 2022. "Toward an efficient hybrid method for pricing barrier options on assets with stochastic volatility," Papers 2202.07849, arXiv.org.
    5. Andrey Itkin & Dmitry Muravey, 2023. "American options in time-dependent one-factor models: Semi-analytic pricing, numerical methods and ML support," Papers 2307.13870, arXiv.org.

    More about this item

    Keywords

    Mathematical Finance; Generalized Integral Transforms; Heat Potentials; Semi-Closed Form Solutions; Advanced Analytics; Barrier Options; Time-Dependent Barrier; Moving Boundaries; American Options; Partial Differential Equations; First Hitting Time Density;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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