Futures trading with transaction costs Karel Janecek Steven Shreve 10.1184/R1/6477506.v1 https://kilthub.cmu.edu/articles/journal_contribution/Futures_trading_with_transaction_costs/6477506 <p>A model for optimal consumption and investment is posed whose solution is provided by the classical Merton analysis when there is zero transaction cost. A probabilistic argument is developed to identify the loss in value when a proportional transaction cost is introduced. There are two sources of this loss. The first is a loss due to “displacement” that arises because one cannot maintain the optimal portfolio of the zero-transaction-cost problem. The second loss is due to “transaction,” a loss in capital that occurs when one adjusts the portfolio. The first of these increases with increasing tolerance for departure from the optimal portfolio in the zero-transaction-cost problem, while the second decreases with increases in this tolerance. This paper balances the marginal costs of these two effects. The probabilistic analysis provided here complements earlier work on a related model that proceeded from a viscosity solution analysis of the associated Hamilton–Jacobi–Bellman equation.</p> 2010-01-01 00:00:00 Mathematical Sciences