Graduate Theses and Dissertations (2019 - present)

Date of Award

12-2025

Document Type

Thesis

Degree Name

M.S.

Department

Mathematics

Committee Chair

Paramahansa Paramanik, Ph.D.

Advisor(s)

Gayan Abeynanda, Ph.D., Vasiliy A. Prokhorov, Ph.D., Martin Frank, Ph.D.

Abstract

This paper explores how established firms use strategic advertising to deter new competitors in uncertain markets. Specifically, it models a situation where market demand evolves unpredictably - captured by the CKLS stochastic process, and the incumbent firm may be either strong or weak, a fact hidden from potential entrants. For a company already in the market, advertising is not just about driving immediate sales, it is a strategic tool to project an image of strength and deter potential new competitors. On the other side, a business thinking about entering that market faces a high-stakes, irreversible decision. It will typically hold back, waiting until customer demand reaches a proven level before taking the plunge. Our research uses an advanced analytical model to pinpoint the strategies each side uses. The findings reveal that less-established market leaders often adjust their spending reactively as demand changes, while newcomers time their entry based on the signals they observe. To ground this theory in reality, we applied our model to actual revenue data from the energy sector, demonstrating just how much the unpredictability of market demand shapes both competitive advertising and the critical decision of when to enter.

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