Numerical Schemes for Variational Inequalities Arising in International Asset Pricing

This paper introduces a valuation model of international pricing in the presence of political risk. Shipments between countries are charged with shipping costs and the country specific production processes are modelled as diffusion processes. The political risk is modelled as a continous time jump process that affects the drift of the returns in the politically unstable countries. The valuation model gives rise to a singular stochastic control problem that is analyzed numerically. The fundamental tools come from the theory of viscosity solutions of the associated Hamilton–Jacobi–Bellman equation which turns out to be a system of integral-differential Variational Inequalities with gradient constraints.