A two-mode mean-field optimal switching problem for the full balance sheet

Boualem Djehiche, Ali Hamdi

Research output: Contribution to journalArticlepeer-review


We consider the problem of switching a large number of production lines between two modes, high production and low production. The switching is based on the optimal expected profit and cost yields of the respective production lines and considers both sides of the balance sheet. Furthermore, the production lines are all assumed to be interconnected through a coupling term, which is the average of all optimal expected yields. Intuitively, this means that each individual production line is compared to the average of all its peers which acts as a benchmark. Due to the complexity of the problem, we consider the aggregated optimal expected yields, where the coupling term is approximated with the mean of the optimal expected yields. This turns the problem into a two-mode optimal switching problem of mean-field type, which can be described by a system of Snell envelopes where the obstacles are interconnected and nonlinear. The main result of the paper is a proof of a continuous minimal solution to the system of Snell envelopes, as well as the full characterization of the optimal switching strategy.

Original languageEnglish (US)
Article number159519
JournalInternational Journal of Stochastic Analysis
StatePublished - 2014

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Modeling and Simulation
  • Applied Mathematics


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