We investigate the incentives for capacity investments in a simple strategic dynamic model with random demand growth. We construct non-collusive Markovian equilibria where the firms' decisions depend on the current capacity stock only. The firms maintain small reserve margins and high market...

We consider a quasilinear parabolic equation with quadratic gradient terms. It arises in the modelling of an optimal portfolio which maximizes the expected utility from terminal wealth in incomplete markets consisting of risky assets and non-tradable state variables. The existence of solutions...