Optimal order execution under price impact: a hybrid model

In this paper we explore optimal liquidation in a market populated by number of heterogeneous makers that have limited inventory-carrying and risk-bearing capacity. We derive reduced form model for the dynamics their aggregated inventory considering proper scaling limit. The resulting price impact profile is shown to depend on characteristics relative importance inventories. flexible enough reproduce empirically documented power law behavior function. For any choice characteristics, execution within modeling approach can be recast as linear-quadratic stochastic control problem. value function associated trading rate obtained semi-explicitly subject solving differential matrix Riccati equation. Numerical simulations are conducted illustrate performance strategy relation standard benchmarks. Remarkably, they show increase determined substantial reduction higher order moment risk.