You retain ownership of the content you put in our system; everything you write is yours. Your intellectual property remains private and your own. You can read more about our policies in our terms and in our FAQ (https://www.quantopian.com/faq and https://www.quantopian.com/policies/terms)
Of course, there is no way that we can prove or guarantee that we're not peeking. Like anything else in the cloud, at some point it becomes a matter of trust. That's why we did our About page a bit differently (https://www.quantopian.com/about). We're all startup veterans with reputations in the industry. You can click the links there and find out who we know in LinkedIn, and see what they say about us. We hope that our good reputations make it easier for you to trust us. Of course, that is entirely up to you!