Intrinsic risks of managing multiple enterprises: a simple deterministic model highlighting unstable patterns

Paper Details

Authors: Dipierro S.; Valdinoci E.

DOI: 10.3934/QFE.2026010

Journal: Quantitative Finance and Economics

Year: 2026

Publisher: American Institute of Mathematical Sciences

Document Type: Article

Open Access: All Open Access; Gold Open Access; Green Open Access

Cited by: 0

Abstract

In this paper, we present a simplified mathematical model using a system of ordinary differential equations to describe the relationships between money flow, staff size, and the number of enterprises managed by a corporation. Despite ignoring external shocks, our stability analysis reveals inherent instabilities in the system, highlighting significant risks for both venture success and staff employment. This model aims to support risk management by emphasizing the intrinsic sensitivity and potential instability in managing multiple enterprises. The methodology is based on the analysis of a system of differential equations, and the major contributions are a novel mathematical model and an explicit stability analysis with relevance to real-world situations. © 2026 the Author(s), licensee AIMS Press.

Keywords

corporate growth; intrinsic instability; multiple enterprises; ordinary differential equations; risk management

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