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The purpose of this paper is to provide a systematic review of literature on corporate engagement with start-ups (CEWS) by identifying the modes, contexts, antecedents, barriers and outcomes. As an emerging field, CEWS presently has no such review available which will help in building consensus within the field and shape future research directions.

The study followed a two-phased systematic review of literature. Three research databases (i.e. Web of Science, ScienceDirect and SCOPUS) were accessed to gather and conduct the review. Of the total 379 papers retrieved, 63 total relevant papers were studied and analysed. The exhaustive review of literature helped to uncover the contexts, perspectives, antecedents, outcomes and barriers reported across the different modes of CEWS.

The study highlighted the five prominent modes of CEWS favoured by large corporations and start-ups. It found that the large corporations and start-ups associate with one another on the basis of complementarities of activities, resources and motives to pursue their strategic orientations. The engagements also face barriers on the ground, such as incompatibility of goals, power imbalances, cultural differences and weak engagement plans. Most important contexts seen were the high-technology industries in the developed economies like the USA and Europe. It also found that ecosystem creation, accessing innovation and corporate strategy have been preferred as the most productive modes of CEWS in the literature.

This review provides practitioners with a detailed list of the modes and drivers of CEWS. Subsequently, the barriers that need to be managed to successfully execute a specific mode of engagement. This shall enable the practitioners in developing and adopting the best practices while engaging with the start-ups to better facilitate the outcomes of CEWS.

To the best of the authors’ knowledge, there is no systematic literature review available in the domain of CEWS – thus, this study makes an important methodological contribution to the field. By consolidating the fragmented yet growing knowledge on CEWS, the study presents a detailed understanding of what drives and obstructs the engagement between large corporations and start-ups.

Identifying the complementary effects of ride-sharing on public transit is critical to understanding the potential value of growing partnerships between public transit agencies and ride-sharing platforms. The purpose of this paper is to investigate whether and how ride-sharing services complement public transit.

Taking advantage of a natural experiment whereby subway Line 2 opened after the entry of ride-sharing services in Xiamen, this study uses a difference-in-differences approach to identify the complementary effects of ride-sharing on public transit based on a proprietary fine-grained trip-level data set from a large ride-sharing platform.

This study obtained the encouraging finding that ride-sharing has a significant complementary effect on the subway, as the number of ride-sharing pickups and drop-offs at subway stations increased by 130% and 117.9%, respectively, after the subway opening. Moreover, mechanism analysis shows that the complementary effect of ride-sharing services is stronger when connection distance is short (i.e. under 6 km) and when the transportation availability is limited (i.e. at night or in the areas with low transit supply and low population density).

The findings provide guidelines for promoting cooperation between public transit agencies and ride-sharing platforms to build an efficient and sustainable urban transport system.

This study is the first to examine the complementary effect of ride-sharing services on public transit via unique fine-grained ride-sharing trips data, and further reveal the underlying mechanism behind this effect.

The purpose of the study is to assess if a policy of female inclusive education should be complemented with a policy of female ownership of bank accounts to fight female unemployment. The study therefore examines how female ownership of bank accounts moderates the incidence of female education on female unemployment.

The focus is on 44 sub-Saharan African (SSA) countries for the period 2004–2018 and the empirical evidence is based on interactive quantile regressions. The interactions are tailored such that female ownership of bank accounts influences the effect of female inclusive education on female unemployment.

From the empirical findings it is evident that female ownership of bank accounts does not effectively moderate female education in order to reduce female unemployment unless complementary policies are considered. The complementary policies should be in view of boosting the interaction between female education and female bank account ownership in increasing employment opportunities for the female gender and by extension, reducing female unemployment. The invalidity of the moderating effect is robust to the inclusion of more elements in the conditioning information set as well as accounting for other dimensions of endogeneity such as simultaneity and the unobserved heterogeneity. Policy implications are discussed.

This study contributes to the extant literature by assessing how female ownership of bank accounts complements female inclusive education to reduce female unemployment.

We present an approach for pricing American put options with a regime-switching volatility. Our method reveals that the option price can be expressed as the sum of two components: the price of a European put option and the premium associated with the early exercise privilege. Our analysis demonstrates that, under these conditions, the perpetual put option consistently commands a higher price during periods of high volatility compared to those of low volatility. Moreover, we establish that the optimal exercise boundary is lower in high-volatility regimes than in low-volatility regimes. Additionally, we develop an analytical framework to describe American puts with an Erlang-distributed random-time horizon, which allows us to propose a numerical technique for approximating the value of American puts with finite expiry. We also show that a combined approach involving randomization and Richardson extrapolation can be a robust numerical algorithm for estimating American put prices with finite expiry.

This paper aims to explore the effect of gender diversity and female empowerment on a firm’s exploration and exploitation capabilities.

This is an empirical paper. This study investigated the research question in this paper using data on UK Financial Times Stock Exchange 100 firms and OLS regression analysis.

This study found a positive association between senior management gender diversity in the workforce and exploitation and exploration capabilities. Also, female empowerment positively moderates senior management gender diversity’s impact on exploration capability.

This study advises firms aspiring ambidextrous to establish gender diversity – especially at the senior management level – and focus on female empowerment in their organisations.

This paper argued for the role of females in making the organisations ambidextrous by impacting both exploitation and exploration capabilities, which did not receive adequate research attention to date.

This paper aims to address the issue of model discontinuity typically encountered in traditional Denavit-Hartenberg (DH) models. To achieve this, we propose the use of a local Product of Exponentials (POE) approach. Additionally, a modified calibration model is presented which takes into account both kinematic errors and high-order joint-dependent kinematic errors. Both kinematic errors and high-order joint-dependent kinematic errors are analyzed to modify the model.

Robot positioning accuracy is critically important in high-speed and heavy-load manufacturing applications. One essential problem encountered in calibration of series robot is that the traditional methods only consider fitting kinematic errors, while ignoring joint-dependent kinematic errors.

Laguerre polynomials are chosen to fitting kinematic errors and high-order joint-dependent kinematic errors which can avoid the Runge phenomenon of curve fitting to a great extent. Levenberg–Marquard algorithm, which is insensitive to overparameterization and can effectively deal with redundant parameters, is used to quickly calibrate the modified model. Experiments on an EFFORT ER50 robot are implemented to validate the efficiency of the proposed method; compared with the Chebyshev polynomial calibration methods, the positioning accuracy is improved from 0.2301 to 0.2224 mm.

The results demonstrate the substantial improvement in the absolute positioning accuracy achieved by the proposed calibration methods on an industrial serial robot.

This study presents a two-step numerical iteration method specifically designed to solve absolute value equations. The proposed method is valuable and efficient for solving absolute value equations. Several numerical examples were taken to demonstrate the accuracy and efficiency of the proposed method.

We present a two-step numerical iteration method for solving absolute value equations. Our two-step method consists of a predictor-corrector technique. The new method uses the generalized Newton method as the predictor step. The four-point open Newton-Cotes formula is considered the corrector step. The convergence of the proposed method is discussed in detail. This new method is highly effective for solving large systems due to its simplicity and effectiveness. We consider the beam equation, using the finite difference method to transform it into a system of absolute value equations, and then solve it using the proposed method.

The paper provides empirical insights into how to solve a system of absolute value equations.

This paper fulfills an identified need to study absolute value equations.

In this paper, the authors study the nonlinear matrix equation Xp=Q±A(X-1+B)-1AT, that occurs in many applications such as in filtering, network systems, optimal control and control theory.

The authors present some theoretical results for the existence of the solution of this nonlinear matrix equation. Then the authors propose two iterative schemes without inversion to find the solution to the nonlinear matrix equation based on Newton's method and fixed-point iteration. Also the authors show that the proposed iterative schemes converge to the solution of the nonlinear matrix equation, under situations.

The efficiency indices of the proposed schemes are presented, and since the initial guesses of the proposed iterative schemes have a high cost, the authors reduce their cost by changing them. Therefore, compared to the previous scheme, the proposed schemes have superior efficiency indices.

Finally, the accuracy and effectiveness of the proposed schemes in comparison to an existing scheme are demonstrated by various numerical examples. Moreover, as an application, by using the proposed schemes, the authors can get the optimal controller state feedback of $x(t+1) = A x(t) + C v(t)$.

In this study, a dynamic contracting model is developed between a venture capitalist (VC) and an entrepreneur (EN) to explore the influence of asymmetric beliefs regarding output-relevant parameters, agency conflicts and complementarity on the VC's posterior beliefs through the EN's unobservable effort choices to influence the optimal dynamic contract.

The authors construct the contracting model by incorporating the VC's effort, which is ignored in most studies. Using backward induction and a discrete-time approximation approach, the authors solve the continuous-time contract design problem, which evolves into a nonlinear ordinary differential equation (ODE).

The optimal equity share that the VC provides to the EN decreases over time. In accordance with the empirical evidence, the EN's optimistic beliefs regarding the project's profitability positively affect its equity share. However, the interactions between the optimal equity share, project risk and both partners' degrees of risk aversion are not monotonic. Moreover, the authors find that the optimal equity share increases with the degree of complementarity, which indicates that the EN is willing to cooperate with the VC. This study’s results also show that the optimal equity shares at each time are interdependent if the VC is risk-averse and independent if the VC is risk-neutral.

In conclusion, the authors highlight two potential directions for future research. First, the authors only considered a single VC, whereas in practice, a risk project may be carried out by multiple VCs, and it is interesting to discuss how the degree of complementarity affects the number of VCs that ENs contract. Second, the authors may introduce jumps and consider more general multivariate stochastic volatility models for output dynamics and analyze the characteristics of the optimal contracts. Third, further research can deal with other forms of discretionary output functions concerning complementarity, such as Cobb–Douglas and constant elasticity of substitution (See Varian, 1992).

The results of this study have several implications. First, it offers a novel approach to designing dynamic contracts that are specific and easy to operate. To improve the complicated venture investment situation and abate conflict between contractual parties, this study plays a good reference role. Second, the synergy effect proposed in this study provides a theoretical explanation for the executive compensation puzzle in economics, in which managers are often “rewarded for luck” (Bertrand and Mullainathan, 2001; Wu et al., 2018). This result indicates a realistic perspective on financing and establishing cooperative relationships, which enhances the efficiency of venture investment. Third, from an empirical standpoint, one can apply this framework to study research and development (R&D) problems.

First, the authors introduce asymmetric beliefs and Bayesian learning to study the dynamic contract design problem and discuss their effects on equity share. Second, the authors incorporate the VC's effort into the contracting problem, and analyze the synergistic effect of effort complementarity on the optimal dynamic contract.