Stochastic control on the half-line and applications to the optimal dividend/consumption problem
Optimization and Control
2025-03-24 v3 Analysis of PDEs
Probability
Portfolio Management
Abstract
We consider a stochastic control problem with the assumption that the system is controlled until the state process breaks the fixed barrier. Assuming some general conditions, it is proved that the resulting Hamilton Jacobi Bellman equations has smooth solution. The aforementioned result is used to solve the optimal dividend and consumption problem. In the proof we use a fixed point type argument, with an operator which is based on the stochastic representation for a linear equation.
Keywords
Cite
@article{arxiv.1703.07339,
title = {Stochastic control on the half-line and applications to the optimal dividend/consumption problem},
author = {Dariusz Zawisza},
journal= {arXiv preprint arXiv:1703.07339},
year = {2025}
}
Comments
The paper is not well written and contains numerous gaps and substantial flaws. Much of the material will be transferred to a new paper entitled "Stochastic exit-time control on the half-line over a finite horizon"