Mathematical Finance Seminar
December 7, 2000 , 5:30 PM to 7:00 PM
Agnes Tourin, University of Toronto
Numerical schemes for variational inequalities arising in international
asset pricing
A joint work with Hodder and Zariphopoulou on
numerical schemes for Variational Inequalities arising in international
asset pricing will be presented. We developed a continuous time model of
international
asset pricing in a two-country framework which considers political risk,
that is the uncertainty about future government actions which may impact
the value of firms or welfare of individuals. Recently, we have observed
international asset prices and exchange rates yoyoing up and down in
response to sequences of gouvernment actions. In order to capture this
sort of phenomenon, we model political risk using a stochastic process with
jumps. We formulate this model as a singular stochastic control
problem and the solution of the optimization problem is characterized as the
unique viscosity (weak) solution of the associated Hamilton-Jacobi-Bellman
equation. We then
derive a numerical scheme to compute the asset prices in both
countries, the free boundaries characterizing the trading policies and
a real exchange rate.