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Stability estimates for the multidimensional elliptic obstacle problem
-
Naveed Ahmad
and
Malkhaz Shashiashvili
Published/Copyright:
February 29, 2012
Abstract.
A Hölder type stability estimate in the second order Sobolev space of functions is established for the solution of the elliptic obstacle problem with respect to variations of the coefficients of the corresponding differential operator.
In modern finance, this estimate provides results on the sensitivity of a perpetual American option price with respect to variations of the volatilities in the underlying assets prices. To meet the objective of this paper, the stability result with respect to external force functions, which was proved by
J.-F. Rodrigues under the nondegeneracy condition, is generalized to the case of arbitrary functions belonging to the space 
, 
.
Keywords.: Unilateral elliptic obstacle problem; stability estimates with respect to the coefficients of a differential operator; sensitivity of perpetual American option prices with respect to volatilities
Received: 2011-04-02
Published Online: 2012-02-29
Published in Print: 2012-March
© 2012 by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Masthead
- Stability estimates for the multidimensional elliptic obstacle problem
- On the two-point boundary value problems for linear impulsive systems with singularities
- Explicit solutions of the boundary value problems of the theory of consolidation with double porosity for the half-plane
- Convergence of modification of the Durrmeyer type -Baskakov operators
- Backward stochastic differential equations with a convex generator
- On some ideal defined by density topology in the Cantor set
- Maximal operator of the Fejér means of triangular partial sums of two-dimensional Walsh–Fourier series
- Fixed point theorems for hybrid mappings satisfying an integral type contractive condition
- On the nonexistence of blowing-up solutions to a fractional functional-differential equation
- Two-weight inequalities for multilinear maximal operators
- An asymptotic model of a nonlinear adaptive orthotropic elastic rod
- Approximation of functions on locally compact abelian groups
