私有 is more general for 'private ownership', while 自己所有 emphasizes that the owner is oneself (the subject).
自己保有 is similar but often used for holding assets or securities, whereas 自己所有 is broader for tangible property.
Compound of 自己 (self) and 所有 (ownership). The exact historical derivation is uncertain, but it follows a common Sino-Japanese word-formation pattern.