Managing Inventory with Proportional Transaction Costs

Abstract

We solve the problem of optimal inventory management for a CARA market-maker who faces proportional transaction costs and marking to market. Our model accommodates inventory shocks following an arbitrary compound Poisson process, and allows us to link the optimal policy to the moment-generating function of the shock distribution. We show that the no-trade region is always wider in the presence of shocks, and depends non-monotonically on the order imbalance. Our findings suggest that optimal accounting for inventory shocks leads to significant utility gains.

Keywords: Inventory Management, Market Making, Transaction Costs

JEL Classification: G24, G32, G11, D92, C61