A double obstacle problem in an optimal investment problem

In this paper, we study a double obstacle problem in partial differential equation that arises in an optimization problem in finance. Precisely, we consider the double obstacle problem which is related to the optimal investment problem with proportional transaction costs of an investor with the logarithmic utility in finite time under the constant elasticity of variance (CEV) model. First, we construct a solution of the double obstacle problem and prove the monotonicity of its free boundaries. From the solution to the double obstacle problem, we construct the solution of the optimization problem. Hence, our result regarding monotonicity indicates the optimal strategy for the optimization problem. & COPY; 2023 Elsevier Ltd. All rights reserved.

Automated summary

In this paper, we study a double obstacle problem in a partial differential equation that arises in an optimization problem in finance. We construct a solution for the double obstacle problem and prove the monotonicity of its free boundaries. From this solution, we can determine the optimal strategy for the optimization problem.