On the relation between the stock market liquidity and the traders' utility: introducing an iteraction among orders

Abstract

In stock markets, it is often argued that increased liquidity contributes to the public benefit of the market as a whole, but it is not self-evident. In this study, we analyze the impact of increasing market liquidity on traders' utility mathematically. We calculate an exact solution of an average expected utility for one trader by using a simple model in which we assume orders follow independent uniform distributions. However, even when we assume a more complicated model where orders interact with each other, we obtain the result consistent with the first simple model in the limit of infinite number of orders. Also, we define a balance price on the order book, and we analyze the behavior of the balance price.