Stochastic inverse problems for growth models

Modern macroeconomics is built on the foundation of nonlinear dynamic stochastic general equilibrium (DSGE) models. In particular, the stochastic growth model is one of the most widely used models in all economics, and is the standard model for business cycle analysis. After reviewing some classical results on the existence of optimal solutions to stochastic calculus of variational problems in finite and infinite horizon, we show the connexions between those kind of problems and some classical stochastic optimal capital growth. Finally, we find some first results on the indeterminacy of capital accumulation path with uncertainty, which generalize the ones obtained by Boldrin and Montrucchio.