Portfolio Execution with Multi-Period Stochastic Forecasts and Size Constraints

Abstract

This paper investigates the problem of finding a dynamically updating trading schedule for a portfolio with stochastically evolving forecasts, absolute value based execution costs and a decaying market impact as well as size constraints. This is achieved by deriving a continuous time stochastic state evolution model as well as a Hamiltonian with a corresponding HJB equation which is then approximately solved to third order accuracy which provides a Value function and the optimal controls.