Portfolio optimization with early announced discrete dividends

In this article we include discrete dividends in the stock price model and solve the corresponding generalized portfolio optimization problem. For this, we develop a new discrete dividend model that allows for the possibility of early announcement and ensures that the drop of the stock price at the ex-dividend date equals the dividend. The resulting portfolio problem can be solved explicitly for both the wealth and the trading strategy. We find that the resulting optimal portfolio process differs from the Merton strategy.