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

Serena Dipierro; Enrico Valdinoci; Serena Dipierro; Enrico Valdinoci

doi:10.3934/QFE.2026010

Quantitative Finance and Economics

2026, Volume 10, Issue 2: 224-244. doi: 10.3934/QFE.2026010

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Research article

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

Serena Dipierro ,
Enrico Valdinoci ^,

Department of Mathematics and Statistics, The University of Western Australia, 35 Stirling Highway, Crawley WA 6009, Australia

Received: 09 October 2025 Revised: 25 December 2025 Accepted: 30 January 2026 Published: 14 April 2026
JEL Codes: L25, M54, D21, C02, C62, C30

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.
- corporate growth,
- multiple enterprises,
- risk management,
- intrinsic instability,
- ordinary differential equations
Citation: Serena Dipierro, Enrico Valdinoci. Intrinsic risks of managing multiple enterprises: a simple deterministic model highlighting unstable patterns[J]. Quantitative Finance and Economics, 2026, 10(2): 224-244. doi: 10.3934/QFE.2026010

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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.

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