Mathematics – Analysis of PDEs
Scientific paper
2011-09-06
Mathematics
Analysis of PDEs
115 pages
Scientific paper
The Heston stochastic volatility process, which is widely used as an asset price model in mathematical finance, is a paradigm for a degenerate diffusion process where the degeneracy in the diffusion coefficient is proportional to the square root of the distance to the boundary of the half-plane. The generator of this process with killing, called the elliptic Heston operator, is a second-order degenerate elliptic partial differential operator whose coefficients have linear growth in the spatial variables and where the degeneracy in the operator symbol is proportional to the distance to the boundary of the half-plane. With the aid of weighted Sobolev spaces, we prove existence, uniqueness, and global regularity of solutions to stationary variational inequalities and obstacle problems for the elliptic Heston operator on unbounded subdomains of the half-plane. 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.
Daskalopoulos Panagiota
Feehan Paul M. N.
No associations
LandOfFree
Existence, uniqueness, and global regularity for degenerate elliptic obstacle problems in mathematical finance does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Existence, uniqueness, and global regularity for degenerate elliptic obstacle problems in mathematical finance, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Existence, uniqueness, and global regularity for degenerate elliptic obstacle problems in mathematical finance will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-92903