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.
