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

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.

55 pages, 1 figure. To appear in Advances in Differential Equations. Incorporates final galley proof corrections corresponding to published version

References in corpus (4)

• A Schauder approach to degenerate-parabolic partial differential equations with unbounded coefficients
• Schauder a priori estimates and regularity of solutions to boundary-degenerate elliptic linear second-order partial differential equations
• C^{1,1} regularity for degenerate elliptic obstacle problems
• Existence, uniqueness, and global regularity for degenerate elliptic obstacle problems in mathematical finance

Cited by in corpus (1)

• Schauder a priori estimates and regularity of solutions to boundary-degenerate elliptic linear second-order partial differential equations