2018/05/28 by David Mguni, Mguni, David
Economics, Econometrics and Finance · #Climate Change Policy and Economics #FOS: Mathematics #Merger and Competition Analysis #Optimization and Control (math.OC) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1805.11974
openalex publication_date 2018/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we study two-player investment problems with investment costs that are bounded below by some fixed positive constant. We seek a description of optimal investment strategies for a duopoly problem in which two firms invest in advertising projects to abstract market share from the rival firm. We show that the problem can be formulated as a stochastic differential game in which players modify a jump-diffusion process using impulse controls. We prove that the value of the game may be represented as a solution to a double obstacle quasi-variational inequality and derive a PDE characterisation (HJBI equation) of the value of the game. We characterise both the saddle point equilibrium and a Nash equilibrium for the zero-sum and non-zero-sum payoff games.