Regions with carbon emission regulations bear the risk of "carbon leakage'' if local producers shift production capacity to an unregulated region. We investigate the problem for a producer subject to geographically asymmetric emission regulation with uncertain future emission price. The producer has two ex-ante options to lower its compliance cost: investing in clean production technology in the regulated region and building production capacity in the unregulated region. The producer determines its production quantities ex-post, after emission price uncertainty is resolved. We study two anti-leakage policies, Border Tax (BT) and Output-Based Allocation (OB), where the former adopts a "stick'' approach that penalizes offshore production and the latter adopts a "carrot'' approach that grants free emission allowances for production in the regulated region. First, we show that the emission price uncertainty can exert opposing effects in the absence of an anti-leakage policy: When the expected emission price is low (high), a higher uncertainty aggravates (mitigates) carbon leakage. Second, through a comprehensive comparison, we highlight that while both BT and OB are able to reduce carbon leakage, BT has a stronger effect in both the regulated and unregulated regions in multiple dimensions, especially when the carbon leakage risk is high. Third, we find that a higher emission price uncertainty weakens the effect of both BT and OB. We therefore suggest that emission price uncertainty should be accounted for when formulating anti-leakage policies. Finally, we extend our analysis to a competitive case and find that the superiority of BT relative to OB is enhanced.