Quadratic Backward Stochastic Differential Equations (BSDEs) Driven by a Continuous Martingale and Application to the Utility Maximization Problem

Marie Amélie Morlais (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

In this paper, we will study some Backward Stochastic Differential Equations (BSDEs) in a continuous filtration which arise naturally in the problem of utility maximization with constraints on the portfolio. In a first part, we will show existence and uniqueness for those BSDEs. Then, we will give an application to the utility maximization problem for three different cases : the exponential utility function, the power one and the logarithmic one.

Mots clés: constraint portfolio; Backward Stochastic Differential Equations; continuous filtration; quadratic growth; utility maximization; incomplete market

Domaines: Probabilités [math.PR]

Marie Amélie Morlais. Quadratic Backward Stochastic Differential Equations (BSDEs) Driven by a Continuous Martingale and Application to the Utility Maximization Problem. Finance and Stochastics, 2009, 13 (1), pp.121-150. ⟨hal-00020254v2⟩