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Applied Mathematics & Optimization· 2026Q1

Long-Term Average Impulse Control with Mean Field Interactions

Kurt Helmes, Richard H. Stockbridge, Chao Zhu

Short summary

This paper explicitly solves long-term average impulse control problems for a one-dimensional diffusion process with mean-field interactions, establishing an equilibrium strategy and a cooperative control solution.

AI-generated from the title and abstract; the full text is not read.

Key points

  • Solves long-term average impulse control problems for general one-dimensional diffusions with mean-field interactions.
  • Establishes and characterizes an equilibrium strategy in a competitive market setting.
  • Formulates and solves a cooperative mean-field control problem for maximal common profit.
  • Illustrates theoretical results with stochastic logistic and population growth models.

AI-generated from the title and abstract; the full text is not read.

Abstract

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.

The authors' abstract, as published at the source. Applied Mathematics & Optimization, 2026 · DOI ↗

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Field: Economics and Econometrics

Economics and EconometricsEconomics, Econometrics and Finance