  We show that in an equity market model with Knightian uncertainty regarding
the relative risk and covariance structure of its assets, the arbitrage
function -- defined as the reciprocal of the highest return on investment that
can be achieved relative to the market using nonanticipative strategies, and
under any admissible market model configuration -- is a viscosity solution of
an associated Hamilton-Jacobi-Bellman (HJB) equation under appropriate
boundedness, continuity and Markovian assumptions on the uncertainty structure.
This result generalizes that of Fernholz and Karatzas (2011), who characterized
this arbitrage function as a classical solution of a Cauchy problem for this
HJB equation under much stronger conditions than those needed here.
