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We consider the problem of maximizing the utility of consumption and terminal wealth in a geometric Ornstein–Uhlenbeck market. We calculate the optimal consumption and wealth processes for power, logarithmic and exponential utility as well as their behavior depending e.g. on subjective discounting or the time horizon. We also use a specific example to show the identity of the solutions calculated by the primal and the dual method.

A note on optimal consumption and investment in a geometric Ornstein–Uhlenbeck market