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Many practical problems in modern finance can be cast into the framework of stochastic differential equations, so that numerical techniques from engineering can be adapted. The static 1D problem in financial engineering characterized by non-self-adjoint is examined in this paper using the Finite Element Method (FEM). The finite element for the problem mentioned above is established based on Galerkin criterion. And numerical examples, such as first exit time of a geometric Brownian mot ion, and convection-dominated problems, are solved using FEM. The results are compared with analytic solution, FDM respectively. It is shown that high computational accuracy and efficiency are achieved using FEM and this method can be further used in dynamic problem, 2D problem of financial engineering.

A Preliminary Study on the Application of FEM in Financial Engineering Analysis