• 1 Introduction
  • 2 Description of the Model and Notation
  • 2.1 Our main result
  • 3 Preliminary estimates
  • 4 Continuity of the Value Functions
  • 5 The Dynamic Programming Principle
  • 6 Existence of a viscosity solution
  • 6.1 Existence of a viscosity upper solution
  • 6.2 Existence of a viscosity lower solution
  • 7 Uniqueness of the Viscosity Solution
  • 7.1 Logarithmic utility function
  • 7.2 Utility function in the class U
  • 8 Numerical illustrations
  • 8.1 Numerical scheme
  • 8.2 Approximate value function
  • 8.3 Efficient strategy
  • 8.4 Misspecications
  • Acknowledgement
  • References