A Comprehensive Model of Stock Prices: The Role of Bonds, Stocks, and Adaptive Expectations

This research develops a straightforward financial market model featuring a single bond and a single stock, each governed by basic pricing formulas. By applying techniques for solving differential equations, the paper demonstrates that under very mild assumptionssuch as the absence of arbitrage opportunities and rational investor behaviorthe stock price converges to its fundamental value over time. These assumptions ensure that expected returns from the bond and the stock align, illustrating how stock prices adjust in response to market dynamics. The focus is on the application of differential equations to show how the stock price moves toward its intrinsic value. It also provides insights into investor's behavior and market adjustments.