Daily price limits are adopted by many securities exchanges in countries such as the USA, Canada, Japan and various other countries in Europe and Asia, in order to increase the stability of the financial market. These limits confine the price of the financial asset during all trading stages of any trading day to a range, usually determined based on the previous day’s closing price. In this paper we study the portfolio optimization problem with impose the price limit constraint. The dynamic programming technique is applied to derive the Hamilton–Jacobi–Bellman equation and the method of Lagrange multiplier is used to tackle the constraint. Optimization problem solution results, using numerical method show that the equilibrium path of wealth and investment in risky assets has a different way than in the absence of price limits.
