Multiplicative Limit Order Markets with Transient Impact and Zero Spread

We study a multiplicative limit order book model for an illiquid market, where price impact by large orders is multiplicative in relation to the current price, transient over time, and non-linear in volume (market) impact. Order book shapes are specified by general density functions with respect to relative price perturbations. Market impact is mean reverting with possibly non-linear resilience. We derive optimal execution strategies that maximize expected discounted proceeds for a large trader over an infinite horizon in one- and also in two-sided order book models, where buying as well as selling is admitted at zero bid-ask spread. Such markets are shown to be free of arbitrage. Market impact as well as liquidation proceeds are stable under continuous Wong-Zakai-type approximations of strategies.