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The Riccati Equation in Mathematical Finance

โœ Scribed by P.P Boyle; W Tian; Fred Guan

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
270 KB
Volume
33
Category
Article
ISSN
0747-7171

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โœฆ Synopsis

This paper uses ideas from symbolic computation to classify solutions to an important class of problems in mathematical finance and thus provides a linkage between these two fields. We show that Kovacic's concept of closed-form solutions to the Riccati ordinary differential equation can be used to provide a precise mathematical definition that is useful in certain financial models. We extend this definition to a broader class of problems and discuss how these ideas can be usefully applied to practical problems in the finance area. We provide a specific application by developing a new implementation of the Cox-Ingersoll-Ross interest-rate model that may be of practical interest.

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