Despite the growing numbers of forcibly displaced persons worldwide, many people living under conflict choose not to flee. Individuals face two lotteries -- staying or leaving -- characterized by two distributions of potential outcomes. This paper proposes to model the choice between these two lotteries using quantile maximization as opposed to expected utility theory. The paper posits that risk-averse individuals aim at minimizing losses by choosing the lottery with the best outcome at the lower end of the distribution, whereas risk-tolerant individuals aim at maximizing gains by choosing the lottery with the best outcome at the higher end of the distribution. Using a rich set of household and conflict panel data from Nigeria, the paper finds that risk-tolerant individuals have a significant preference for staying and risk-averse individuals have a significant preference for fleeing, in line with the predictions of the quantile maximization model. These findings are contrary to findings on economic migrants, and call for separate policies toward economic and forced migrants.