Application of Financial Mathematical Models in Optimal Pricing Decisions of Monopoly Firms

The pricing decisions of monopoly firms represent a core problem in industrial organization and financial economics, which has significant impaction for market efficiency and consumer welfare. When markets evolve from traditional industrial structures to digital ecosystems, the mathematical modeling of monopoly pricing becomes more sophisticate. Incorporating game-theoretic frameworks, stochastic processes, and optimization techniques. This paper studies how financial mathematical models can support monopoly firms in setting optimal prices. By using the method of comparative analysis, it mainly discusses Cournot competition model, Hotelling spatial competition model, and how these two models are adjusted for adapting to today's market environment. The analysis shows that classical models provide basic understandings into equilibrium pricing under different competitive situations. However, we cannot use these models directly for digital or resources focused markets. People need to change them to consider network effects, algorithm driven dynamic pricing and government rules. The findings suggest that combining stochastic differential equations and game theory can help people to build better pricing models for modern monopoly markets conditions are uncertain. This method also provides some useful suggestions for regulators who hope to keep market efficiency while protecting consumer interests.