Mathematics of Computational Finance

Mathematics of Computational Finance book cover

Mathematics of Computational Finance

Author(s): Andrzej Palczewski (Author)

  • Publisher finelybook 出版社: World Scientific Publishing Company
  • Publication Date 出版日期: October 29, 2025
  • Language 语言: English
  • Print length 页数: 444 pages
  • ISBN-10: 9819815118
  • ISBN-13: 9789819815111

Book Description

The book focuses on numerical methods for derivative pricing with an emphasis on their mathematical foundations. It offers the most frequently explored numerical methods of derivative pricing and covers the material of standard courses in computational finance. The book presents the best-known methods of multinomial trees, Monte Carlo simulations for European, American, and exotic options, and finite difference and finite element methods for PDEs. However, unlike many textbooks on computational finance, it also presents rigorous results on analyzed numerical algorithms with a focus on the mathematical content — including theorems with possibly complete proofs.

The book gives the reader the necessary tools for analyzing algorithm consistency and offers an efficient approach to assessing the stability and convergence of numerical methods. It consolidates mathematical results previously dispersed across different monographs into a single volume, while tailoring the presentation to the specific needs of computational finance.

Each chapter includes a set of exercises designed to help readers apply theoretical concepts to specific algorithms and enhance their computational skills in derivative pricing.

Editorial Reviews

About the Author

Andrzej Palczewski is currently a Professor Emeritus at the University of Warsaw. He earned his MS from the Chemistry Department of the University of Warsaw and his Ph.D. and Habilitation doctorate from the Mathematics Department of the University of Warsaw. In 1993, he was awarded the title of professor by the President of the Polish Republic. From 1968 to 1970, he was a staff member of the Institute of Nuclear Research, and from 1973 to 1975, he was at the Institute of Mathematics, Warsaw Technical University. In 1975, he moved to the University of Warsaw, where he was employed until 2018 as a Professor of Mathematics.

Professor Palczewski's current research interests are primarily in the mathematical modeling of financial markets, with an emphasis on the computational aspects of considered models. For a long time, his research concentrated on problems related to equations in mathematical physics, including quantum mechanics, statistical physics, and fluid mechanics. He has authored over 60 research papers and many educational articles, co-authored two monographs, and authored two textbooks.

Professor Palczewski was Deputy Dean of the Faculty of Mathematics, Informatics and Mechanics at the University of Warsaw from 1984 to 1986, and he served as Director of the Institute of Applied Mathematics and Mechanics at the University of Warsaw from 1993 to 1999. He was a member of the editorial boards of several mathematical journals, a member of the Council of the European Consortium for Mathematics in Industry from 1998 to 2008, and from 2011 to 2017, the head of the IFIP TC 7 Working Group "Modeling and Simulation".

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