Degenerate-elliptic operators in mathematical finance and higher-order regularity for solutions to variational equations
We establish higher-order weighted Sobolev and Holder 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.
|Date of creation:||Aug 2012|
|Date of revision:||Nov 2014|
|Publication status:||Published in Advances in Differential Equations 20 (2015), no. 3/4, 361-432|
|Contact details of provider:|| Web page: http://arxiv.org/|
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- 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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