Quadratic BSDEs driven by a continuous martingale and application to utility maximization problem

Details Quadratic BSDEs driven by a continuous martingale and application to utility maximization problem Quadratic BSDEs driven by a continuous martingale and application to utility maximization problem

2006-10-25

arxiv.org/abs/math/0610749v3

Mathematics

Probability

Scientific paper

In this paper, we study a class of quadratic Backward Stochastic Differential Equations (BSDEs) which arises naturally when studying the problem of utility maximization with portfolio constraints. We first establish existence and uniqueness results for such BSDEs and then, we give an application to the utility maximization problem. Three cases of utility functions will be discussed: the exponential, power and logarithmic ones.

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