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Price limits set up are adopted by many securities markets in countries such as the USA, Canada, Japan, and various other countries in Europe and Asia, to increase the stability of the financial market. These limits confine the price of the financial asset during 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 while taking into account 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 and numerical method show that the equilibrium path of wealth and investment in risky assets has a different pattern than the absence of price limits.

Optimal portfolio allocation with imposed price limit constraint