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Obstacle problems for nonlocal operators
by
Danielli, Donatella
, Pop, Camelia A.
, Petrosyan, Arshak
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Obstacle problems for nonlocal operators
by
Danielli, Donatella
, Pop, Camelia A.
, Petrosyan, Arshak
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Obstacle problems for nonlocal operators
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Overview
We prove existence, uniqueness, and regularity of viscosity solutions to the stationary and evolution obstacle problems
defined by a class of nonlocal operators that are not stable-like and may have supercritical drift. We give sufficient
conditions on the coefficients of the operator to obtain Hölder and Lipschitz continuous solutions. The class of nonlocal
operators that we consider include non-Gaussian asset price models widely used in mathematical finance, such as Variance Gamma
Processes and Regular Lévy Processes of Exponential type. In this context, the viscosity solutions that we analyze coincide with
the prices of perpetual and finite expiry American options.
Publisher
American Mathematical Society
ISBN
9781470441104, 1470441101
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