Crowdfunding is a new financing method that is widely utilized by start-up firms and adds to the traditional financing channels such as bank loans. We consider the optimal financing problem for a start-up firm with an innovative product, i.e., when to utilize crowdfunding and/or bank loans to maximize profits, given that both the crowdfunding capital supply and retail market demand are uncertain, with potential correlations. We find four types of financing strategies
: single-source (crowdfunding only) and dual-source (crowdfunding and bank loan) financing, with prudent/aggressive goal-setting in crowdfunding. The four strategies each can be optimal for a specific parameter range regarding the relative magnitude of crowdfunding v.s. retail markets and the cost of crowdfunding. In addition, we derive comparative statics with respect to the post-campaign market demand, the crowdfunding market demand, the bank loan interest rate, and analyze their impacts on the optimal financing strategy. In the extension we highlight how uncertainty weighs in the decision-making process by analyzing a counter-factual complete information model, and further analyze how the correlation between crowdfunding and retail market affects the optimal financing strategy.