A Survey of the Optimal Consumption-Investment Problem with Transaction Costs

Abstract

This article is a review paper on Merton’s portfolio problem with transaction costs. This problem has been of great interest to many researchers since it was first raised in the 1970s. After many years of trial and error and research progress, this article addresses the studies that have made the greatest contribution to solving the problem, in historical order. After a detailed description of the problem formulation, we focus on the ideas of analytical methods to solve the problem as well as the economic interpretation of optimal consumption and investment.