Numerical Solution of Dynamic Portfolio Optimization with Transaction Costs

We apply numerical dynamic programming techniques to solve discrete-time multi-asset dynamic portfolio optimization problems with proportional transaction costs and shorting/borrowing constraints. Examples include problems with multiple assets, and many trading periods in a finite horizon problem. We also solve dynamic stochastic problems, with a portfolio including one risk-free asset, an option, and its underlying risky asset, under the existence of transaction costs and constraints. These examples show that it is now tractable to solve such problems.