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

Asymptotics of the probability minimizing a "down-side" risk