This paper develops a model of arbitrage trading on assets with fat-tail risks. When arbitrageurs are uncertain about the variance of fat-tailed mispricings, they choose to ignore a wide range of opportunities under the max-min criterion. Even though model risk hinders their willingness to act, arbitrageurs can catch the most profitable trades by their linear, momentum trading outside the inaction region. We show that this equilibrium strategy is observationally equivalent to the LASSO regression which finds solid, Bayesian-rational grounds in this paper. Arbitrageurs can amass extra market power due to conservative trading. Their strategic exercise of robust control facilitates a cartel, protecting their profits from being competed away even when their population goes to infinity. Those results shed light on a new mechanism for limits to arbitrage.