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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-...
Stochastic representation of solutions to degenerate elliptic and parabolic boundary value and obstacle problems with Dirichlet boundary conditions
Degenerate elliptic and parabolic differential operators degenerate diffusion process Feller square root process Feynman-Kac formula
2012/4/28
We prove stochastic representation formulae for solutions to elliptic and parabolic boundary value and obstacle problems associated with a degenerate Markov diffusion process. In particular, our artic...
On a class of semi-elliptic diffusion models. Part I: a constructive analytical approach for global existence, densities, and numerical schemes
Degenerate parabolic equations financial derivatives
2010/10/18
Semi-elliptic stochastic differential equations (SDEs) are common models among practitioners. However, value functions and sensitivities of such models are described by degenerate parabolic partial d...