A stochastic overlapping generation model with a continuum of agents

Abstract

To cite this version:Emmanuelle Augeraud-Véron, Delphine David. A stochastic overlapping generation model with a continuum of agents. Lukasz Stettner. Advances in Mathematics of Finance, Apr 2007, Bedlewo, Poland. 83, pp.27-36, 2008 A stochastic overlapping generation model with a continuum of agentsAbstract We consider a stochastic overlapping generations model for a continuum of individuals with finite lives in presence of a financial market. In this paper, agent's heterogeneity is given by the dates of birth of the households, on the contrary to standard models, in which each agent has his own aversion coefficient on his utility function. By means of the martingale arguments, we compute the agent's optimal consumption and portfolio. A characterization of interest rate trajectories is given by mixed-type functional differential equations and the stability of these trajectories is studied.