We consider portfolio selection problems in an environment with nonconvex transaction costs and capital gains taxes. Nonconvex transaction costs arise when discounted commission rates are offered on larger trades, or a flat fee is charged in addition to a percentage of the trade value. In this context, we study the following portfolio selection problem: given a tax and transaction cost environment, how much of each asset in a given collection should be bought or sold, so that some measure of portfolio value is optimized? We study the problem from the point of view of both risk-neutral and risk-averse investors, using both single- and multiperiod time horizons.; For risk-neutral investors, we establish properties of the problem's structure, and we derive exact optimal solutions for several special cases. We also derive heuristics for the general case.; For risk-averse investors, we propose three approximation algorithms for solving nonconvex generalizations of the Markowitz model. Finally, we propose a multiperiod risk-averse model using the technique of scenario trees. We also propose a model for choosing parameters for the scenario trees using observations of stock market data.; We test all models in this thesis numerically.
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