Dynamic equilibrium problems under debt constraints, contingent asset pricing problems.

Summary The first part deals with dynamic equilibrium problems under debt constraints. More precisely, it presents two models, one in a one-country economy, the other in a two-country economy, in which agents are subject to stochastic variations in productivity against which they can only imperfectly insure themselves, because of the presence of debt constraints. The consequences are the appearance, in the first case, of fluctuations in aggregate variables, and in the second case, of correlations between the economic quantities of the two countries, phenomena that would be absent in a complete market. The second part deals with mathematical problems concerning the valuation of contingent assets. We solve two option pricing models that depend on the history of the underlying price. We also present a model of the yield curve under imperfect information.