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Spline Cubatures for Expectations of Diffusion Processes and Optimal Stopping in Higher Dimensions (with Computational Finance in View)

In: Mathematical Control Theory and Finance

Author

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  • Andrew Lyasoff

    (Boston University, Mathematical Finance Program)

Abstract

Summary We develop certain cubature (quadrature) rules for expectations of diffusion processes in ℝ N that are analogous to the well known spline interpolation quadratures for ordinary integrals. By incorporating such rules in appropriate backward induction procedures, we develop new numerical algorithms for solving free-boundary (optimal stopping) problems, or ordinary fixed-boundary problems. The algorithms developed in the paper are directly applicable to pricing contingent claims of both American and European types on multiple underlying assets.

Suggested Citation

  • Andrew Lyasoff, 2008. "Spline Cubatures for Expectations of Diffusion Processes and Optimal Stopping in Higher Dimensions (with Computational Finance in View)," Springer Books, in: Andrey Sarychev & Albert Shiryaev & Manuel Guerra & Maria do Rosário Grossinho (ed.), Mathematical Control Theory and Finance, pages 265-291, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-69532-5_15
    DOI: 10.1007/978-3-540-69532-5_15
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