Utility maximization in incomplete markets with default

Thomas Lim (1) , Marie-Claire Quenez (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We adress the maximization problem of expected utility from terminal wealth. The special feature of this paper is that we consider a financial market where the price process of risky assets can have a default time. Using dynamic programming, we characterize the value function with a backward stochastic differential equation and the optimal portfolio policies. We separately treat the cases of exponential, power and logarithmic utility.

Mots clés: Utility maximization; dynamic programming; backward stochastic differential equation; default time; incomplete market

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

Thomas Lim, Marie-Claire Quenez. Utility maximization in incomplete markets with default. 2008. ⟨hal-00342531v3⟩