  In this paper we study the optimization problem of an economic agent who
chooses a job and the time of retirement as well as consumption and portfolio
of assets. The agent is constrained in the ability to borrow against future
income. We transform the problem into a dual two-person zero-sum game, which
involves a controller, who is a minimizer and chooses a non-increasing process,
and a stopper, who is a maximizer and chooses a stopping time. We derive the
Hamilton-Jacobi- Bellman quasi-variational inequality(HJBQV) of a max-min type
arising from the game. We provide a solution to the HJBQV and verification that
it is the value of the game. We establish a duality result which allows to
derive the optimal strategies and value function of the primal problem from
those of the dual problem.
