Optimal Conic Execution Strategies with Stochastic Liquidity

In this paper, we develop the conic finance framework for optimal execution of a large portfolio in an illiquid market. We extend the classical optimal execution results by considering stochastic exogenous liquidity effects as well as temporary price impact functions. We depart from the traditionally assumed linear impact function and introduce both stochastic liquidity and volatility effects and nonlinear temporary market impact. Moreover, we allow for an additional stochastic exogenous liquidity effect, used to capture the base illiquidity of a market. We analyze various aspects of our model using a stylized example