by Philip H. Dybvig and Hyeng-Keun Koo

**Abstract**

A serious analysis of taxes makes optimization models of investments much more complicated and more interesting. Because the portfolio strategy and value function depend on the holdings in each security at each tax basis, it is difficult to solve these problems exactly. Even numerical solutions are difficult except for very small problems, given the size of the state space and the necessary path-dependence of the strategies. This paper formulates some investment problems with taxes and presents their numerical solution for some simple examples.