The Exponential Habit Forming Utility: Explicit Forms and Graphical Illustrations

  • Author / Creator
    Lu, Boyuan
  • This thesis focuses on characterizing the optimal consumption and investment strategy for an investor, in a simple financial market, when his consumption habit is considered in the utility formulation. We consider a continuous-time market model for which we maximize the overall utility within an infinite horizon. Using the Bellman's Principle, we derive the associated Hamilton-Jacobi-Bellman equation (called HJB hereafter). For the case of HARA utility (exponential, power and logarithmic), the solution to the corresponding HJB is explicitly described. Furthermore, for the HARA case, the optimal consumption, consumption habit and wealth processes are described by a stochastic differential equation (called SDE hereafter). We pay particular attention to the case of exponential utility, where the obtained SDE is solved explicitly. By applying graphing method, we explain the relationships between the optimal consumption/wealth/habit and the system's parameters. This result is meaningful, since it implies the potential influence to investors when the system's parameters are changing.

  • Subjects / Keywords
  • Graduation date
  • Type of Item
  • Degree
    Master of Science
  • DOI
  • License
    This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.
  • Language
  • Institution
    University of Alberta
  • Degree level
  • Department
    • Department of Mathematical and Statistical Sciences
  • Specialization
    • Mathematical Finance
  • Supervisor / co-supervisor and their department(s)
    • Tahir, Choulli (Mathematical and Statistical Sciences)
  • Examining committee members and their departments
    • Abel Cadenillas (Mathematical and Statistical Sciences)
    • Peter Minev (Mathematical and Statistical Sciences)
    • Christoph Frei (Mathematical and Statistical Sciences)
    • Tahir Choulli (Mathematical and Statistical Sciences)