As of lately I have been going through many research papers in my current job, and even though I have a Mathematics background at Masters level in Mathematical Finance, I sometimes struggle to follow some arguments in numerical analysis.
The research always involves an stochastic component, as these papers are mainly related to Probability theory applied to finance. A clear example of the situation is this paper.
My question is mostly aimed at people who hold PhD degrees in Physics or Mathematics. Can you recommend me a well-respected book in numerical analysis that would help me better grasp the reasoning behind advanced numerical arguments like the paper above mentioned?
You may refer to the following book. Non-Linear Option Pricing co-authored by Pierre Henry Labordere recipient of 'Quant of the year 2013'.
It clearly explains the BSDE approach to solve parabolic pdes of first and second order and draws out the discretization schema in detail. It also contains financial applications of this approach.
In addition to this, it contains several non-linear methods (HJB, stochastic control, particle method, optimal stopping time problem etc).
Edit: Second reference
Computational Methods in Finance