Abstract
We consider the problem of utility maximization in a Black-Scholes market in the presence of proportional transaction costs. While it is well-known that the value function of this problem is the unique viscosity solution of the corresponding Hamilton-Jacobi-Bellman (HJB) equation (cf. Belak et al. (2013)), and that the HJB equation admits a classical solution on a reduced state space (cf. Dai and Yi (2009)), it has been an open problem to construct the optimal strategies. We provide a simple method to prove the existence of the candidate optimal strategies, verify their optimality, study the regularity in detail and show that value function coincides with the classical solution of the HJB on the reduced state space.
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.
