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

Viscosity Characterization of the Arbitrage Function under Model Uncertainty