Optimal Market-Making with Risk Aversion

Market-makers have the obligation to trade any given amount of assets at quoted bid or ask prices, and their inventories are exposed to the potential loss when the market price moves in an undesirable direction. One approach to reduce the risk brought by price uncertainty is to adjust the inventory at the price of losing potential spread gain. Using stochastic dynamic programming, we show that a threshold inventory control policy is optimal with respect to an exponential utility criterion and a mean-variance trade-off model. Symmetric and monotone properties of the threshold levels are also established.