This book shows the power of the separation of variables technique by solving a variety of problems, many of which go well beyond the usual textbook problems. With a focus on the potential, heat, and wave equations throughout the book, the authors take a spectral expansion view of the technique and explore it in detail. Written at the advanced undergraduate level, the presentation requires a background in engineering mathematics, but no prior exposure to the method. The abundant worked examples provide guidelines for deciding whether and how to apply the method to any given problem, will help...

The early exercise opportunity of an American option makes it challenging to price. The Numerical Solution of the American Option Pricing Problem focuses on three numerical methods that have proved useful for the numerical solution of the partial differential equations with free boundary problem arising in American option pricing, namely the method of lines, the sparse grid approach and the integral transform approach. It clearly explains and demonstrates the advantages and limitations of each of them using several examples.

Few financial mathematical books have discussed mathematically acceptable boundary conditions for the degenerate diffusion equations in finance. In The Time-Discrete Method of Lines for Options and Bonds, Gunter H Meyer examines PDE models for financial derivatives and shows where the Fichera theory requires the pricing equation at degenerate boundary points, and what modifications of it lead to acceptable tangential boundary conditions at non-degenerate points on computational boundaries when no financial data are available.Extensive numerical simulations are carried out with the method of...