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Optimal Investment and Consumption with Fixed and Proportional Transaction Costs

In: Recent Developments In Mathematical Finance

Author

Listed:
  • Hong Liu

    (The Olin School of Business, Washington University, St. Louis, MO 63130, USA)

Abstract

We consider the optimal investment and consumption policy for a constant absolute risk averse investor who faces fixed and/or proportional transaction costs when trading a stock and maximizes his expected utility from intertemporal consumption. We show that the Hamilton-Jacobi-Bellman PDE with free boundaries can be reduced to an ODE, which greatly simplifies the problem. Using the stochastic impulse and singular control techniques, we then derive the optimal investment and consumption policy. In particular, when there are both fixed and proportional costs, it is shown that the optimal stock investment policy is to keep the dollar amount invested in the stock between two constant levels and upon reaching these two thresholds, the investor jumps to the corresponding optimal target level.

Suggested Citation

  • Hong Liu, 2001. "Optimal Investment and Consumption with Fixed and Proportional Transaction Costs," World Scientific Book Chapters, in: Jiongmin Yong (ed.), Recent Developments In Mathematical Finance, chapter 6, pages 60-71, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789812799579_0006
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