  We present turnpike-type results for the risk tolerance function in an
incomplete market setting under time-monotone forward performance criteria. We
show that, contrary to the classical case, the temporal and spatial limits do
not coincide. We also show that they depend directly on the left- and right-end
of the support of an underlying measure, which is used to construct the forward
performance criterion. We provide examples with discrete and continuous
measures, and discuss the asymptotic behavior of the risk tolerance for each
case.
