Abstract
Abstract We analyze a numerical scheme for solving the consumption and investment allocation problem studied in a companion paper by Hindy, Huang, and Zhu (1997). For this problem, Bellman's equation is a variational inequality involving second-order partial differential equation with gradient constraints. The solution involves finding a free-boundary at which consumption occurs. We prove that the value function is the unique viscosity solution to Bellman's equation. We describe a numerical analysis technique based on Markov chain approximation schemes. We approximate the original continuous time problem by a sequence of discrete parameter Markov chains control problems. We prove that the value functions and the optimal investment policies in the sequence of the approximating control problems converge to the value function and the optimal investment policy, if it exists, of the original problem. We also show that the optimal consumption and abstinence regions in the sequence of approximating problems converge to those in the original problem.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
