  In this note, we give a brief overview of obstacle problems for nonlocal
operators, focusing on the applications to financial mathematics. The class of
nonlocal operators that we consider can be viewed as infinitesimal generators
of non-Gaussian asset price models, such as Variance Gamma Processes and
Regular L\'evy Processes of Exponential type. In this context, we analyze the
existence, uniqueness and regularity of viscosity solutions to obstacle
problems which correspond to prices of perpetual and finite expiry American
options. Complete proofs can be found in arXiv:1709.10384, where these results
have originally appeared.
