  We determine the optimal robust investment strategy of an individual who
targets at a given rate of consumption and seeks to minimize the probability of
lifetime ruin when she does not have perfect confidence in the drift of the
risky asset. Using stochastic control, we characterize the value function as
the unique classical solution of an associated Hamilton-Jacobi-Bellman (HJB)
equation, obtain feedback forms for the optimal investment and drift
distortion, and discuss their dependence on various model parameters. In
analyzing the HJB equation, we establish the existence and uniqueness of
viscosity solution using Perron's method, and then upgrade regularity by
working with an equivalent convex problem obtained via the Cole-Hopf
transformation. We show the original value function may lose convexity for a
class of parameters and the Isaacs condition may fail. Numerical examples are
also included to illustrate our results.
