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Abstract

Motivated by downside risk minimization on the wealth process in an incomplete market model, we have studied in the recent work the asymptotic behavior as time horizon $T\to \infty$ of the minimizing probability that the empirical mean of a controlled semi-martingale falls below a certain level on the time horizon $T$. This asymptotic behavior relates to a risk-sensitive stochastic control problem in the risk-averse case. Indeed, we obtained an expression of the decay rate of the probability by the Legendre transform of the limit value of the value function of the stochastic control problem, which is characterized as the solution to the H–J–B equation of ergodic type. In the current work we present the results on its robust version, admitting model uncertainty.