Using Chebyshev polynomials to approximate partial differential equations. (English) Zbl 1182.93119
Summary: This paper suggests a simple method based on a Chebyshev approximation at Chebyshev nodes to approximate Partial Differential Equations (PDEs). It consists in determining the value function by using a set of nodes and basis functions. We provide two examples: pricing a European option and determining the best policy for shutting down a machine. The suggested method is flexible, easy to programme and efficient. It is also applicable in other fields, providing efficient solutions to complex systems of PDEs.
MSC:
| 93E20 | Optimal stochastic control |
| 91G20 | Derivative securities (option pricing, hedging, etc.) |
| 90B30 | Production models |
| 41A50 | Best approximation, Chebyshev systems |
Software:
CompEconReferences:
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