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Degenerate-elliptic operators in mathematical finance and higher-order regularity for solutions to variational equations
Campanato space degenerate-elliptic di erential operator degenerate di usion process Heston stochastic volatility process Holder regularity mathematical nance Schauder a priori estimate Sobolev regularity variational equation weighted Sobolev space.
2012/9/17
We establish higher-order weighted Sobolev and Holder regularity for solutions to variational equations de ned by the elliptic Heston operator, a linear second-order degenerate-elliptic operator aris...
C^{1,1} regularity for degenerate elliptic obstacle problems in mathematical finance
American-style option degenerate elliptic di erential operator degenerate di usion process, free boundary problem Heston stochastic volatility process mathematical nance obstacle problem variational inequality weighted Sobolev space.
2012/9/14
The Heston stochastic volatility process is a degenerate di usion process where the degeneracy in the di usion coecient is proportional to the square root of the distance to the boundary of the half-...
Regularity of the Optimal Stopping Problem for Levy Processes with Non-Degenerate Diffusions
Regularity Levy Processes Non-Degenerate Diffusions
2010/10/29
The value function of an optimal stopping problem for a process with L´evy jumps is known to be a generalized solution of a variational inequality. Assuming the diffusion component of the proces...
Existence & Regularity of Weak Solutions of Degenerate Parabolic PDE Models for the Pricing of Security Derivatives
Existence Regularity Weak Solutions Security Derivatives
2010/10/29
This work is focused on the solvability of initial-boundary value problems for degenerate parabolic partial differential equations that arise in the pricing of Asian options, and
on the investigation...