Advances in Differential Equations
- Adv. Differential Equations
- Volume 20, Number 3/4 (2015), 361-432.
Degenerate-elliptic operators in mathematical finance and higher-order regularity for solutions to variational equations
We establish higher-order weighted Sobolev and Hölder 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.
Adv. Differential Equations, Volume 20, Number 3/4 (2015), 361-432.
First available in Project Euclid: 4 February 2015
Permanent link to this document
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35J70: Degenerate elliptic equations 49J40: Variational methods including variational inequalities [See also 47J20] 35R45: Partial differential inequalities 60J60: Diffusion processes [See also 58J65]
Feehan, Paul M.N.; Pop, Camelia A. Degenerate-elliptic operators in mathematical finance and higher-order regularity for solutions to variational equations. Adv. Differential Equations 20 (2015), no. 3/4, 361--432. https://projecteuclid.org/euclid.ade/1423055204