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