Abstract:This paper analyzes and explicitly solves a class of long-term average impulse control problems with a specific mean-field interaction. The underlying process is a general one-dimensional diffusion with appropriate boundary behavior. The model is motivated by applications such as the optimal long-term management of renewable resources and financial portfolio management. Each individual agent seeks to maximize her long-term average reward, which consists of a running reward and income from discrete impulses, where the unit intervention price depends on the market through a stationary supply rate, the specific mean field variable to be considered. In a competitive market setting, we establish the existence of and explicitly characterize an equilibrium strategy within a large class of policies under mild conditions. Additionally, we formulate and solve the mean field control problem, in which agents cooperate with each other, aiming to realize a common maximal long-term average profit. To illustrate the theoretical results, we examine a stochastic logistic growth model and a population growth model in a stochastic environment with impulse control.
From: Chao Zhu [view email]
[v1]
Fri, 16 May 2025 15:12:48 UTC (59 KB)
[v2]
Tue, 20 Jan 2026 02:30:08 UTC (41 KB)
[v3]
Tue, 3 Feb 2026 15:41:53 UTC (41 KB)
[v4]
Thu, 16 Jul 2026 15:18:28 UTC (39 KB)
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