The incentive effect of venture capital in bilateral partnership systems with the bias mono-stable Cobb–Douglas utility

The decision‐making of optimal equity and capital structure based on dynamical risk profiles: A Langevin system framework for SME growth

“…We start considering an SME characterized by the bilateral partnership system, typically including technology-side S T (who has the original idea, patents, or some exclusive knowledge to pursuit the successful development of new product at capital-to-product stage) and marketingside S M (who has some previously accumulated business expertize, contacts, or reputation to achieve the cash-return at product-to-capital stage). 19,20 It is supposed that the SME is established with total capital C t , which is originally composed of internal paid-in capital C p and inward venture capital C v . In the allocation of productive elements, it is the prerequisite and foundation for SME growth to improve capital structure.…”

“…We start considering an SME characterized by the bilateral partnership system, typically including technology‐side (who has the original idea, patents, or some exclusive knowledge to pursuit the successful development of new product at capital‐to‐product stage) and marketing‐side (who has some previously accumulated business expertize, contacts, or reputation to achieve the cash‐return at product‐to‐capital stage) 19,20 …”

“…The dynamical behavior can be described by the following over‐damped Langevin equation: where is the state associated with cooperation and competition in the process of SME growth, is the damping coefficient, and each term in Equation (14) is explained as follows: represents the inherent tech‐economic paradigm of bilateral partnership in the limit of capital‐constraint . It produces the utility force with gradient form to pull SME state to reside in the local equilibria of bistable utility potential field 19,20,23 mimics the periodic driving force associated with normalized adjustable input capital .…”

“… represents the inherent tech‐economic paradigm of bilateral partnership in the limit of capital‐constraint . It produces the utility force with gradient form to pull SME state to reside in the local equilibria of bistable utility potential field 19,20,23 …”

“…Based on linear response theory, unit risk‐return (URR) performance is proposed under the measurement of stationary systematic risk, bilateral cooperation risk. Further, Yu et al 20 proposed an extended system with bistable utility structure, and tried to answer the questions of how the venture capital motivated the partners especially associated with partnership success, what roles the internal and external risks played respectively. It was found that the interplay between periodic effect from operating capital and stochastic fluctuation associated with internal and external environment could effectively drive SMEs to regularly switches between capital and technology equilibria, and produce the maximum of stochastic incentive effect in the statistical sense.…”