Upcoming Book on PDE Methods in Finance (planned date December 2021)
Daniel J. Duffy, PhD
Author/trainer/mentor in computational finance: maths (pure, applied, numerical), ODE/PDE/FDM, C++11/C++20, Python, C#, modern software design
NUMERICAL METHODS IN COMPUTATIONAL FINANCE
A Partial Differential Equation (PDE/FDM) Approach
Daniel J. Duffy
Part A Mathematical Foundation for One-Factor Problems
1.???????????Real Analysis Foundations for this Book
2.???????????Topics in Ordinary Differential Equations and their Applications
3.???????????An Introduction to Two-Point Boundary Value Problems
4.???????????An Introduction to Finite Dimensional?Vector Spaces and Matrix Theory
5.???????????Guide to Numerical Linear Algebra
6.???????????Numerical Solutions of Two-Point Boundary Value Problems
7.???????????Black Scholes Finite Differences for the Impatient
Part B Mathematical Foundation for Two-Factor Problems
8.???????????Classifying and Transforming Partial Differential Equations
9.???????????An Introduction to Elliptic Partial Differential Equations
10.?????????Boundary Value Problems for Elliptic Partial Differential Equations
11.?????????Elliptic Equations?and the Fichera Theory
12.?????????An Introduction to Time-dependent Convection-Diffusion-Reaction Equations
13.?????????Stochastics Representations of PDEs and Applications
Part C The Foundations of the Finite Difference Method (FDM)
14.?????????Mathematical and Numerical Foundations of the Finite Difference Method, Part I
15.????????? Mathematical and Numerical Foundations of the Finite Difference Method Part II
16.?????????Sensitivity Analysis, Option Greeks and Parameter Optimisation
17. ????????Advanced Topics in Sensitivity Analysis
Part D Advanced Finite Difference Schemes for Two-Factor Problems
18.?????????Splitting Up Methods, Part I
19.?????????The Alternating Direction Explicit (ADE) Method in Detail
20.?????????The Method of Lines (MOL)
21.?????????Free and Moving Boundary Value Problems
22.?????????Splitting Up Methods, Part II
Part E Test Cases in Computational Finance
23.?????????Multi-Asset Options
24.???????Asian-Style Options
25.?????????Interest Rate Models
26.?????????Epilogue: Follow-up to Chapters 1 to 25
27. ????????New Project Areas
CEO & Co-Founder at Reactive Capital
3 年Wow. This book is my next must read??????
Author/trainer/mentor in computational finance: maths (pure, applied, numerical), ODE/PDE/FDM, C++11/C++20, Python, C#, modern software design
3 年here is the slide show of my talk at Thalesians next Wednesday. https://www.datasim.nl/application/files/1416/2964/2727/PDE_and_FDM_in_Computational_Finance_25_August_2021OFFICIAL.pdf
Author/trainer/mentor in computational finance: maths (pure, applied, numerical), ODE/PDE/FDM, C++11/C++20, Python, C#, modern software design
3 年For those interested I have the honour of giving a tall for the Thalesians August 25 2021.
Author/trainer/mentor in computational finance: maths (pure, applied, numerical), ODE/PDE/FDM, C++11/C++20, Python, C#, modern software design
3 年This book is aimed at a wide audience, but it should be of particular interest to MSc and MFE students as well as quants in computational finance. In particular, there are opportunities for new research projects and applications to production systems. We give guidelines on which scheme is optimal (in terms of accuracy, applicability, robustness and maintainability) for a given problem in computational finance.