does he own any production company?
No.
Introduction
Throughout his career, Hutcherson has expressed an interest in directing and producing. 
who is josh hutcherson? He is an American actor and producer.
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Josh Hutcherson [SEP] Introduction
In 2011, he landed the leading role of Peeta Mellark in the box office record-setting film series "The Hunger Games", released annually from 2012 to 2015, for which he won three MTV Movie Awards and a People's Choice Award. During the same period he also played a lead role in "" (2012) and a voice role in the animated film "Epic" (2013). Throughout his career, Hutcherson has expressed an interest in directing and producing. He has served as an executive producer in "Detention" (2011), "The Forger" (2012) and "" (2015), while also playing a lead role in each film. He is also heavily involved in the gay–straight alliance chapter called "Straight But Not Narrow".