This thesis contains several lines of research conducted during my four years at the European University Institute. It deals with two distinct topics in the area of recursive economies, developed in three chapters. The first chapter considers a general class of recursive models in which inequality constraints pose a challenging problem: Standard Dynamic Programming techniques often necessitate a non established differentiability of the value function, while Euler equation based techniques have problematic or unknown convergence properties. The second chapter studies a model of optimal redistribution policies in which agents face unemployment risk and in which savings may provide partial self-insurance. Moral hazard arises as job search effort is unobservable. The optimal redistribution policies provide new insights into how an unemployment insurance scheme should be designed. The third chapter studies a very similar model to that explored in Chapter 2. In contrast, however, I impose a liquidity constraint that limits agents' possibility to borrow. As will be shown, this additional constraint will have salient quantitative implication on how an optimal unemployment insurance programme should be designed.
