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Pricing futures by deterministic methods. (English) Zbl 1272.91122
Summary: In this article we will focus on only a small part of financial mathematics, namely the use of partial differential equations for pricing futures. Even within this narrow range it is hard to be systematic and complete, or even to do better than existing books such as [P. Wilmott et al., The mathematics of financial derivatives. A student introduction. Cambridge: Cambridge Univ. Press (1995; Zbl 0842.90008); Y. Achdou and O. Pironneau, Computational methods for option pricing. Philadelphia, PA: Society for Industrial and Applied Mathematics (SIAM) (2005; Zbl 1078.91008)], or software manuals. So this article may be valuable only to the extent that it reflects ten years of teaching, conferences and interaction with the protagonists of financial mathematics.
Also, because the theory of partial differential equations is not always well known, we have chosen a pragmatic approach and left out the details of the theory or the proofs of some results, and refer the reader to other books. The numerical algorithms, on the other hand, are given in detail.
MSC:
91G20 Derivative securities (option pricing, hedging, etc.)
91G80 Financial applications of other theories
35Q91 PDEs in connection with game theory, economics, social and behavioral sciences
91G60 Numerical methods (including Monte Carlo methods)
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