Functional Limit Theorems for a Simple Auction
研究连续透明拍卖中买卖双方到达、交易和挂单行为的随机过程，推导出这些过程在适当缩放下的极限分布，对理解拍卖动态和价格形成有理论价值。
We consider a continuous transparent auction with one asset. Buyers and sellers arrive at the auction according to independent renewal processes, willing to transact a random number of units (shares) of the asset for one of N possible prices. Upon arrival, they buy/sell as many units of the asset as they can for the best price available at that time. However, if the prices offered for sale/purchase are worse than their initial preferences, they do not transact, but instead they stay at the auction, posting buying/selling orders and waiting for a suitable counterparty. We model the numbers of outstanding orders of each type, together with the numbers of assets exchanged up to date by customers of different types, by stochastic processes and find the limiting distributions of these (suitably scaled) processes.