Presentation: 2025 ND EPSCoR Annual conference 

October 21, 2025, NDSU Memorial Union, Fargo, North Dakota

A Markovian Framework for Discrete Stock Price Dynamics with a Reflecting Lower Boundary

This project develops a discrete stochastic model for stock price dynamics using a Markovian framework with fixed price increments. The price can move upward or downward by a fixed amount, with a reflecting lower boundary at the market opening price to prevent falling below its initial value. Future price movements depend only on the current price, and the rates of upward and downward moves are state-dependent, with holding times at each price level exponentially distributed. The model’s analytical properties, including transition probabilities, expected hitting times, and stationary distributions, are explored. A simple example with a maximum of two upward price movements (N=2) is presented, illustrating explicit calculations of probabilities and expected waiting times. This example demonstrates how discrete stochastic modeling can capture key aspects of price behavior and provides a clear framework for understanding discrete price dynamics in financial markets.