A market model: uncertainty and reachable sets

• Published in: International journal for simulation and multidisciplinary design optimization Vol. 6; p. A2
• Main Author: Raczynski, Stanislaw
• Format: Journal Article
• Language: English
• Published: Les Ulis EDP Sciences 2015
• Subjects: Differential inclusions; Human behavior; Inclusions; Investment strategy; Market model; Marketing; Markets; Mathematical models; Parameter uncertainty; Simulation; Statistical analysis; Uncertainty
• ISSN: 1779-627X; 1779-6288; 1779-6288
• DOI: 10.1051/smdo/2015002

Uncertain parameters are always present in models that include human factor. In marketing the uncertain consumer behavior makes it difficult to predict the future events and elaborate good marketing strategies. Sometimes uncertainty is being modeled using stochastic variables. Our approach is quite different. The dynamic market with uncertain parameters is treated using differential inclusions, which permits to determine the corresponding reachable sets. This is not a statistical analysis. We are looking for solutions to the differential inclusions. The purpose of the research is to find the way to obtain and visualise the reachable sets, in order to know the limits for the important marketing variables. The modeling method consists in defining the differential inclusion and find its solution, using the differential inclusion solver developed by the author. As the result we obtain images of the reachable sets where the main control parameter is the share of investment, being a part of the revenue. As an additional result we also can define the optimal investment strategy. The conclusion is that the differential inclusion solver can be a useful tool in market model analysis.