Kelly criteria for a wealth process to reach a goal are studied under ambiguous market. Issues of how ambiguity of market parameters affect portfoliomanagement are investigated. I show that ambiguity aversion of a rationalindividual decreases her market participation when return and volatility areuncorrelated, and there is a small exception for synchronous return and volatility. The aggregate premium of being short a discounted reward is computedexplicitly which is decomposed into two parts. An investor’s pessimism leadsto negative volatility premium. However the risk premium is positive. As a result, in an underestimated pricing economy, investors could still make positive premium via appropriate allocation among assets.