Please use this identifier to cite or link to this item: http://localhost:80/xmlui/handle/123456789/11970
Title: STABILITY ESTIMATES FOR THE ELLIPTIC AND PARABOLIC OBSTACLE PROBLEMS
Authors: Ahmad, Naveed
Keywords: Natural Sciences
Issue Date: 2006
Publisher: GC University Lahore, Pakistan
Abstract: Stability of the solution of the multidimensional unilateral obstacle problem with respect to the variations of the coefficients of the corresponding second order partial differential operator is studied in the present thesis. A H ̈lder type stability estimate in the second order Sobolev space of functions is o established for the solution of the elliptic obstacle problem. Rodrigues ([25, 1987]) proved the stability result with respect to bounded external force functions under the nondegeneracy condition. We generalize this result to the case of arbitrary functions belonging to the space Lp (D), p ≥ 2. Further parabolic obstacle problem is studied with different principal parts in the parabolic differential operator and applied to the American put option problem with various local volatility functions. The estimate of the area between the early exercise boundaries through the uniform distance between the local volatility functions is obtained.
URI: http://142.54.178.187:9060/xmlui/handle/123456789/11970
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