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

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  • Paul M. N. Feehan
  • Camelia A. Pop

Abstract

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.

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  • Paul M. N. Feehan & Camelia A. Pop, 2012. "Degenerate-elliptic operators in mathematical finance and higher-order regularity for solutions to variational equations," Papers 1208.2658, arXiv.org, revised Nov 2014.
    • Handle: RePEc:arx:papers:1208.2658
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    References listed on IDEAS

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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.
    2. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
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