I am interested in adaptive mesh methods for numerical solution of PDEs with applications to finance. As part of a school project, I have been pricing vanilla European call and put options using 2D FEM (space+time) and successfully applied an adaptive mesh algorithm to reduce the numerical error introduced by non-smooth payoffs.

I have not been able to find a lot of existing work on 2D space-time FEM in finance, let alone adaptive mesh methods in this context. Hence the question: do people tend to use FDMs due to ease of implementation (separate discretisation of the dimensions is much easier to handle code-wise), or are there other reasons for the apparent absence of space-time FEM in the literature?

I am contemplating whether or not it makes sense to keep working in this direction, as the lack of similar papers/works in progress might suggest that it is not of any relevance. If I have missed any existing papers on this topic, please provide references if possible.

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    $\begingroup$ there are a few books, such as "Financial Engineering with Finite Elements", on FEM application in quantitative finance. $\endgroup$ – Gordon Jul 3 '15 at 20:11
  • $\begingroup$ @Gordon : I am familiar with this book, but it only addresses spatial FEM as far as I can tell. $\endgroup$ – turtlesandwich Jul 4 '15 at 8:40

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