sth of one’s own
你说的对。own 没有名词词性。但是它有代词词性。代词起名词作用。
英汉词典的解释:
own: 代词
〔起名词作用〕自己的东西[家属、责任、立场(等)];心爱的人。 May I not do what I will with my own? 我自己的东西难道不能随意处理吗? May I have it for my (very) own? 我可以拿它当做我自己专有的东西吗? My own did not believe it. 连我家里的人也不相信。 And his own received him not. 他的家属也不容他。 my own(我的)乖乖〔爱称〕。 come into one's own 取得属于自己的财产[东西];获得应有的名誉[信用等]。 do it on one's own 照自己的意思[由自己负责]做事。 get (a bit of) one's own back 〔口语〕雪耻,报仇。 hold one's own 坚持自己立场,固守立场,不屈服(The patient is holding his own. 病人还照常支持)。 love (truth) for its own sake 为(真理)而爱(真理)。 of one's own 自己的,自己所有的(She had never had a room of her own. 她从来没有自己的住房)。 on one's own (account) 〔俚语〕独自地;独立地;凭自己力量;主动地;自愿地。 with one's own eye 亲眼(看见)。