Stochastic Dynamical Framework for Risk Managements of SMEs’ Growth: Model, Approach and Quantitative Analysis
摘要
This study aims to establish an interpretable prototype system by describing the development and growth mechanisms of small and micro enterprises (SMEs) under a tech-economic paradigm by applying the stochastic dynamical system approach with the associated stochastic resonance theory. It will also develop an associated quantitative method of risk management and growth optimization under the measurement of systematic response risk, bilateral cooperation risk, and value at response risks (VaRR) performance. From the perspective of bistable stochastic resonance (SR), as the inherent regularity of capital-product switches is applied together with both capital-related driving and input risk stimulating, the system is driven by the combination of the forces that compete and cooperate to produce an optimal control on response risk compression or VaRR improvement. Furthermore, based on the real-world supporting profiles from the manufacturing sector in China, we investigate the validity by developing different strategies from micro profile adjustment, mesoscopic structure control, and macro climate regulation. It is found that any strategies are not always effective, and some non-monotonic phenomena are even against the intuitions, which are results of stochastic resonance features caused by the stochastic dynamical system. These findings suggest that, with the integrative consideration of specialization level, management orientation, scale preference, and strategic partner, they can play a more critical role, which provides the crucial quantitative support, and further leads us to create useful decision rules in risk management practices. Finally, we hope the framework established in this study may provide some mathematical fundamentals to explain SME’s growth with innovation for Schumpeter’s economic development theory introduced around 1910’s.