Our problem is motivated by an exchange rate control problem, where the control is composed of a direct impulsive intervention and an indirect, continuously acting intervention given by the control of the domestic interest rate. Similarly to [2] we formulate it as a mixed classical-impulse control problem. Analogously to [2], our approach builds on a quasi-variational inequality, which we consi...

A zero-sum stochastic differential game problem on infinite horizon with continuous and impulse controls is studied. We obtain the existence of the value of the game and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities. We also obtain a verification theorem which provides an optimal strategy of the game. Mathematics Subject Classificati...

0