Dynamic M&A strategy: Modeling optimal acquisition timing using Brownian motion

This paper investigates the optimal strategy for mergers and acquisitions (M&A) within corporate finance. We assume that two role model companies significantly influence the effort levels of other companies. As the effort level affects a company's future rate of return, we model this rate using Brownian motion to determine the optimal timing for M&A. Through this approach, we derive the optimal M&A strategy, specifying when and how much to acquire. Two illustrative examples are provided to demonstrate constructive acquisition strategies. This research contributes to the literature by offering a theoretical framework that optimizes M&A strategy, particularly regarding acquisition timing and scale, in a stochastic environment.