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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-...
Path properties and regularity of affine processes on general state spaces
affine processes path properties regularity Markov semimartingales
2011/7/20
We provide a new proof for regularity of affine processes on general state spaces by methods from the theory of Markovian semimartingales. On the way to this result we also show that the definition of...
Regularity of the Exercise Boundary for American Put Options on Assets with Discrete Dividends
Exercise Boundary Assets Discrete Dividends
2010/11/3
We analyze the regularity of the optimal exercise boundary for the American Put option
when the underlying asset pays a discrete dividend at a known time td during the lifetime of
the option. The ex...
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...