  We consider a long-term optimal investment problem where an investor tries to
minimize the probability of falling below a target growth rate. From a
mathematical viewpoint, this is a large deviation control problem. This problem
will be shown to relate to a risk-sensitive stochastic control problem for a
sufficiently large time horizon. Indeed, in our theorem we state a duality in
the relation between the above two problems. Furthermore, under a
multidimensional linear Gaussian model we obtain explicit solutions for the
primal problem.
