We construct a stochastic model to study the fund matching between fund-raisers and investors in a financing platform. The raising time is assumed to be a random variable. Then, there is a successful transaction probability that the fund matching is realized. Meanwhile, the interest and the commission rate that the platform earns affect the value of the probability. The platform maximizes its revenue by adjusting the commission rate. We find that the optimal commission rate decreases in investment time. However, when the time interval between two adjacent investments obeys the general distribution, the optimal commission rate increases in the annual interest rate. Besides, we extend the model into a duopoly case in which two fund-raisers compete for customers in the same platform by deciding their own interest rate. Due to lacking competition, the optimal interest rate in the monopoly case is lower than that in the duopoly case. Because the interest rate is the cost for the fund-raiser, the expected profit of the fund-raiser in the monopoly is higher than the expected profit of each fund-raiser in the duopoly case but lower than the total expected profit of two fund-raisers. The platform should choose some small loans as far as possible. The loans with smaller amount are easier for the platform to complete fundraising. For those large loans, the platform should try to ask for higher interest rates or more sufficient time to raise funds.
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