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Volume 10, Issue 4

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Dynamic Integration of Interpolating Functions and Some Concrete Optimal Stopping Problems
Andrew Lyasoff

This article describes a streamlined method for simultaneous integration of an entire family of interpolating functions that uses one and the same interpolation grid in one or more dimensions. A method for creating customized quadrature/cubature rules that takes advantage of certain special features of Mathematica's InterpolatingFunction objects is presented. The use of such rules leads to a new and more efficient implementation of the method for optimal stopping of stochastic systems that was developed in [1]. In particular, this new implementation allows one to extend the scope of the method to free boundary optimal stopping problems in higher dimensions. Concrete applications to finance--mainly to American-style financial derivatives--are presented. In particular, the price of an American put option that can be exercised with any one of two uncorrelated underlying assets is calculated as a function of the observed prices. This method is similar in nature to the well-known Longstaff-Schwartz algorithm, but does not involve Monte-Carlo simulation of any kind.

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About the Author
Andrew Lyasoff is director of the Graduate Program in Mathematical Finance at Boston University. His research interests are mainly in the areas of Stochastic Analysis, Optimization Theory, and Mathematical Finance and Economics.

Andrew Lyasoff
Boston University
Mathematical Finance Program
Boston, MA
alyasoff@bu.edu


     
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