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# Degenerate-elliptic operators in mathematical finance and higher-order regularity for solutions to variational equations

## Author Info

• Paul M. N. Feehan
• Camelia Pop
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## Abstract

We establish higher-order weighted Sobolev and H\"older regularity for solutions to variational equations defined by the elliptic Heston operator, a linear second-order degenerate-elliptic operator arising in mathematical finance. Furthermore, given $C^\infty$-smooth data, we prove $C^\infty$-regularity of solutions up to the portion of the boundary where the operator is degenerate. In mathematical finance, solutions to obstacle problems for the elliptic Heston operator correspond to value functions for perpetual American-style options on the underlying asset.

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File URL: http://arxiv.org/pdf/1208.2658
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## Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1208.2658.

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Date of creation: Aug 2012
Date of revision: Feb 2013
Handle: RePEc:arx:papers:1208.2658

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Web page: http://arxiv.org/

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## References

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1. JosE Da Fonseca & Martino Grasselli & Claudio Tebaldi, 2008. "A multifactor volatility Heston model," Quantitative Finance, Taylor & Francis Journals, vol. 8(6), pages 591-604.
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