A stochastic overlapping generation model with a continuum of agents

Emmanuelle Augeraud-Véron (1) , Delphine David (1)

1 LMA-Rochelle - Laboratoire de Mathématiques et Applications

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 tra jectories is studied.

Mots clés: mixed-type functional differential equations; stochastic overlapping generations; mixed-type functional differential equations.

Domaines: Optimisation et contrôle [math.OC]; Probabilités [math.PR]

Emmanuelle Augeraud-Véron, Delphine David. A stochastic overlapping generation model with a continuum of agents. Advances in Mathematics of Finance, Apr 2007, Bedlewo, Poland. pp.27--36. ⟨hal-00373653⟩