Asymptotics of the probability of minimizing ‘down-side’ risk under partial information

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We consider minimizing the probability of falling below a target growth rate of the wealth process up to a time horizon T in an incomplete market model under partial information and then study the asymptotic behavior of the minimizing probability as T → ∞. This problem is closely related to an ergodic risk-sensitive stochastic control problem under partial information in the risk-averse case. Indeed, in our main theorem we relate the former problem to the latter as its dual. As a result we obtain an explicit expression for the limit value of the former problem in the case of linear Gaussian models.