Abstract
In this paper, we study the classical problem of maximization of the sum of the utility of the terminal wealth and the utility of the consumption, in a case where a sudden jump in the risk-free interest rate creates incompleteness. The value function of the dual problem is proved to be solution of a BSDE and the duality between the primal and the dual value functions is exploited to study the BSDE associated to the primal problem.
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