Sample Path Based Optimal Position Liquidation With Cvar Risk

The purpose of this research is to investigate devising the optimal position liquidation strategies in financial markets. During the transaction of large block orders, investors need to maximize their profits against the losses caused by price slippage. We employed a sample-path based stochastic programming approach to obtain a dynamic lower-bound optimal trading strategy with Conditional Value-at-Risk constraint. We analyzed the optimization problems with different types of objective functions determined by distinct market impact functions. Nonanticipativity and risk constraints are discussed and properly imposed to avoid anticipating solutions and to control risk. A new formulation is proposed to obtain a lower-bound of the optimal position liquidation problem. A case study is implemented in the run-file environment of Portfolio Safeguard. Lower-bound optimal strategies are obtained from problems with and without risk constraints. The result also verifies the supposed improvement of computational efficiency in the new formulation.