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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...
We prove existence, regularity and a Feynman-Kaˇc representation formula of the strong solution to the free boundary problem arising in the financial problem of the pricing of the American Asian optio...