Smoothing and parametric rules for stochastic mean-CVaR optimal execution strategy

Computing optimal stochastic portfolio execution strategies under an appropriate risk consideration presents many computational challenges. Using Monte Carlo simulations, we investigate an approach based on smoothing and parametric rules to minimize mean and Conditional Value-at-Risk (CVaR) of the execution cost. The proposed approach reduces computational complexity by smoothing the nondifferentiability arising from the simulation discretization and by employing a parametric representation of a stochastic strategy. We further handle constraints using a smoothed exact penalty function. Using the downside risk as an example, we show that the proposed approach can be generalized to other risk measures. In addition, we computationally illustrate the effect of including risk on the stochastic optimal execution strategy.