I develop a model of portfolio selection in continuous time where transaction costs are random. In the model, the consumer faces a trade off between getting good terms of trade and holding a well balanced portfolio. First, I formulate the relevant co...
I develop a model of portfolio selection in continuous time where transaction costs are random. In the model, the consumer faces a trade off between getting good terms of trade and holding a well balanced portfolio. First, I formulate the relevant control problem and prove that the value function is the unique viscosity solution of the associated Hamilton-Jacoby-Bellman equation. Next, I present a numerical procedure to solve the equation and a proof that the numerical solution converges to the true solution of the problem. The actual implementation of the procedure fully characterizes the optimal consumer behavior.