| Faculty name: | Christina Christara |
|---|---|
| Research area: | Numerical Analysis |
| Campus address: | Bahen 4226 |
| Campus phone: | 416-978-7360 |
| Email address: |
ccc [at] cs.toronto.edu
|
| Number of students: | 1 |
| Skills required: |
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Partial Differential Equations (PDEs) are an indispensable tool in the mathematical modelling of many problems in computational science, engineering and finance. As PDEs arising in the modelling of such problems are often not solvable by analytical mathematical techniques, numerical methods are employed for the approximation of the PDE solution. Then, several interesting questions arise, including (a) how accurate the approximation is, (b) how efficient the numerical method is when implemented as software, (c) what potential the method has to be implemented efficiently on modern parallel architectures, such as Graphics Processing Units (GPUs).
We recently developed models and numerical methods for pricing various financial products, such as American options and Power Reverse Dual Currency (PRDC) swaps. The pricing of such products requires the solution of one or more time-dependent PDEs. Alternating Direction Implicit (ADI) methods were used for the time discretization of PDEs, and standard Finite Difference (FD) methods, mostly on uniform grids, were used for the space discretization. A GPU implementation indicated substantial improvements in execution time.
This project may involve one or more of the following investigations: