Finite-Horizon Optimal Investment with Transaction Costs: Construction of the Optimal Strategies
Posted: 28 Jul 2015 Last revised: 4 Sep 2019
Date Written: May 2, 2018
We revisit the problem of maximizing expected utility of terminal wealth in a Black-Scholes market with proportional transaction costs. While it is known that the value function of this problem is the unique viscosity solution of the HJB equation and that the HJB equation admits a classical solution on a reduced state space, it has been an open problem to verify that these two coincide. We establish this result by devising a verifcation procedure based on superharmonic functions. In the process, we construct optimal strategies and provide a detailed analysis of the regularity of the value function.
Keywords: Utility Maximization, Transaction Costs, Reflected Diffusions, Superharmonic Functions
JEL Classification: G11, C61
Suggested Citation: Suggested Citation