Optimal investment in an illiquid financial market

We introduce a price impact model which accounts for finite market depth, tightness and resilience whose coupled bid- and ask-price dynamics induce convex costs. We provide existence of an optimal solution to the classical... [ view full abstract ]

We introduce a price impact model which accounts for finite market depth, tightness and resilience whose coupled bid- and ask-price dynamics induce convex costs. We provide existence of an optimal solution to the classical problem of maximizing expected utility from terminal liquidation wealth. In the simplest model configuration, it turns out that the resulting singular optimal stochastic control problem reduces to a deterministic problem. Rather than studying the associated Hamilton-Jacobi-Bellmann PDE, we exploit convex analytic techniques allowing us to construct the solution explicitly and to describe the free boundaries of the action- and non-action regions in the underlying state space.