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International Journal of Stochastic Analysis
Volume 2014 (2014), Article ID 159519, 16 pages
Research Article

A Two-Mode Mean-Field Optimal Switching Problem for the Full Balance Sheet

Department of Mathematics, KTH-Royal Institute of Technology, 100 44 Stockholm, Sweden

Received 20 February 2014; Accepted 4 May 2014; Published 25 May 2014

Academic Editor: Qing Zhang

Copyright © 2014 Boualem Djehiche and Ali Hamdi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.