This book is a detailed introduction to the mathematical theory and foundations of ordinary and partial differential equations, their approximation by the finite difference method and applications to computational finance. Major benefits of the book are:
- Step-by-step, incremental build-up of the material.
- Examples and algorithms worked out in detail. Opportunity to modify the algorithms and extend them to your own applications.
- Modern, state-of-the art numerical schemes for PDEs in finance.
- Guidelines on C++ coding (C++11 to C++20); the book is the ideal companion to the author’s book Financial Instrument Pricing Using C++ (second edition, 2018).
- The book is structured so that the material can be applied to a range of existing and new application areas.
- We resolve a number of outstanding issues and improve several less-than-optimal numerical methods in finance.
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