QUALITATIVE-ANALYSIS OF A NONLINEAR STOCK-PRICE MODEL

Attention is focused on stock price models with no closed-form solutio n, the most likely occurrence, when realistic assumptions are made abo ut the sources of dividends. It is argued that these models can supply valuable information for both financial analysis and financial manage ment, provided that they are treated as dynamic systems and tackled ac cordingly by means of a qualitative analysis. As an example, the profi tability of a firm is taken as a state variable within the celebrated model by Gordon and Shapiro. A one parameter bifurcation analysis is p erformed on the ensuing nonlinear dynamic system. Novel results about the price-earnings ratio are obtained and financially interpreted.