Preparing for school

[Quasar Chunawala]

Hi friends,

I am doing some self-learning and considering applying to the local college nearby, for an applied mathematics course.

One of the core courses offered in the 1st semester is - applied PDEs. The professor who teaches the course is an applied mathematician who actually does this stuff - so I am excited and delighted to learn.

I am intent on studying alongside work. To manage the workload better, my strategy is to learn the core courses ahead of time. The ones I have begun reading-up on my own are - mathematical programming(optimization), applied functional analysis and applied PDEs. I had a couple of questions -

1. I am going to use Strauss for linear PDEs, as it appears to give a clear presentation. For non-linear, my colleague recommended: An Introduction to Non-Linear Partial Differential Equations, Logan. Are these okay for an applied course in PDEs? Any recommendations for numerics are welcome.

2. I'd like to do a PDE-based project. Any tips on where I should look for project ideas?

Thanks so much,
Quasar.

 

[Daniel Duffy]

I do PDE/FDM finance project as part of my online courses. If you wait a few months you can see them in my forthcoming book. And many are programmed in my 2018 book Financial Instrument Pricing in C++ (Wiley). One-stop shop

Logan's book is great if you are studying biolgy. A bridge too far to Black Scholes.
But if you have the time for Logan, go for it.. But it misses the mark.

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 in such a way that the material can be applied to a range of existing and new application areas.

. We resolve a number of outstanding issues and we improve several less-than-optimal numerical methods in finance.

ETC....

 

[Daniel Duffy]

2. I'd like to do a PDE-based project. Any tips on where I should look for project ideas?

Project idea do for UnCertain Vol,Heston,SABR.

Here is a very good MSc PDE finance thesis from 2015, supervised by DD.

Quasar; see also www.datasim.nl for theses 2019/2020.

 

[Quasar Chunawala]

I do PDE/FDM finance project as part of my online courses. If you wait a few months you can see them in my forthcoming book. And many are programmed in my 2018 book Financial Instrument Pricing in C++ (Wiley). One-stop shop

Logan's book is great if you are studying biolgy. A bridge too far to Black Scholes.
But if you have the time for Logan, go for it.. But it misses the mark.

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 in such a way that the material can be applied to a range of existing and new application areas.

. We resolve a number of outstanding issues and we improve several less-than-optimal numerical methods in finance.

ETC....

The table of contents for the new edition is really nice. Although, I will purchase the 2018 one right away. I will start bulking up on the fundamentals (Laplace, Poisson and Heat equation) and numerics rather quick.

Will peruse the theses; I actually did see the one which applies the complex step method. One of the things my senior colleague told me, was to start thinking about the theses right off the bat. When I enrol for the course, 18 months is a short time to write a thesis.

 

[Daniel Duffy]

Maths theses need time to incubate, indeed.

Exx. generalise CSM to n dimensions and use it instead of Automatic Differentiation (AD) in ML, especially in gradient descent etc.