This paper studies the optimal portfolio decisions of participants in defined contribution (DC) pension plans who are able to invest their wealth in transnational securities. More specifically, pension participants can allocate their investments across cash, bonds, domestic stocks, foreign stocks, inflation-indexed instruments, and exchange rate futures. Furthermore, we assume that pension managers face ambiguity regarding the distribution of foreign asset prices. In this context, by employing dynamic programming and the "relative entropy penalty" method, the paper derives robust optimal portfolio strategies for DC pension plan participants, accompanied by a verification theorem. Additionally, we explore two specific scenarios: the optimal investment strategy for pension managers under ambiguity neutrality, and the utility loss incurred by ambiguity-averse fund managers who misapply the optimal investment strategy. Our analysis is illustrated through numerical examples.