Abstract
We consider a Barenblatt parabolic equationArising from a financial stochastic optimal control model. In this model, the control variable l, which is bounded and lies in [0, M], should be chosen to optimize the objective function to take the maximum value. From the problem, it can be seen that l should be either 0 or M, which depends on whether vx is greater than 1 or not. We divide the domain into two parts, {vx > 1} and {vx ⩽ 1}. Thus, the junction of the two regions, that is, free boundary, has particular financial implications. It can be expressed as a functional form h(t). In this article, we not only prove the existence and uniqueness of the solution to this equation, but we also study the property of the free boundary h(t). We show that h(t) is a differentiable, nondecreasing function. We also present the shapes of h(t) in different cases. The most difficult point is to prove the concavity of the value function by stochastic analysis.
Sign-in/Register to access full text options 
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.
