We investigate the ergodic problem of growth-rate maximization under a class
of risk constraints in the context of incomplete, It\^{o}-process models of
financial markets with random ergodic coefficients. Including {\em
value-at-risk} (VaR), {\em tail-value-at-risk} (TVaR), and {\em limited
expected loss} (LEL), these constraints can be both wealth-dependent(relative)
and wealth-independent (absolute). The optimal policy is shown to exist in an
appropriate admissibility class, and can be obtained explicitly by uniform,
state-dependent scaling down of the unconstrained (Merton) optimal portfolio.
This implies that the risk-constrained wealth-growth optimizer locally behaves
like a CRRA-investor, with the relative risk-aversion coefficient depending on
the current values of the market coefficients.