Abstract
We give an algorithmic solution of the optimal consumption problem [Formula: see text], where Ct denotes the accumulated consumption until time t, and τ denotes the time of ruin. Moreover, the endowment process Xt is modeled by [Formula: see text]. We solve the problem by showing that the function provided by the algorithm solves the Hamilton-Jacobi (HJ) equation in a viscosity sense and that the same is true for the value function of the problem. The argument is finished by a uniqueness result. It turns out that one has to change the optimal strategy at a sequence of endowment values, described by a free boundary value problem. Finally we give an illustrative example.
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.
