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Many governments are taking measures in support of small and medium-sized enterprises (SMEs) to mitigate the economic impact of the COVID-19 outbreak. This paper presents a theoretical model for evaluating various government measures, including insurance for bank loans, interest rate subsidy, bridge loans and relief of tax burdens.

This paper distinguishes a firm's intrinsic value and book value, where a firm can lose its intrinsic value when it encounters cash-flow crunch. Wang transform is applied to (1) calculating the appropriate level of interest rate subsidy payable to incentivize banks to issue more loans to SMEs and to extend the loan maturity of current debt to the SMEs, (2) describing the frailty distribution for SMEs and (3) defining banks' underwriting capability and overlap index in risk selection.

Government support for SMEs can be in the form of an appropriate level of interest rate subsidy payable to incentivize banks to issue more loans to SMEs and to extend the loan maturity of current debt to the SMEs.

More available data on bank loans would have helped strengthen the empirical studies.

This paper makes policy recommendations of establishing policy-oriented banks or investment funds dedicated to supporting SMEs, developing risk indices for SMEs to facilitate refined risk underwriting, providing SMEs with long-term tax relief and early-stage equity-type investments.

The model highlights the importance of providing bridge loans to SMEs during the COVID-19 disruption to prevent massive business closures.

This paper provides an analytical framework using Wang transform for analyzing the most effective form of government support for SMEs.

In 2002, variable annuities were introduced in South Korea and have shown enormous success since then. They are life-insurance products with investment guarantees. Variable annuities allow policyholders to allocate premiums into a wide range of investment vehicles such as stocks, bonds, money market instruments, or some combinations of them. Due to the investment guarantee which is called guaranteed living benefits (GLBs), the benefit is always the greater of (1) the account value of the policyholder investment and (2) the guaranteed amount. Life insurance companies set aside reserves for the guarantees in the general account. Just as the account value depends on the performance of investments, VA lapses also rely on the performance of investments. For example, policyholders will not terminate the contracts when account value is way lower than the guaranteed amount. Considering that lapses determine the total benefit of VAs that a insurance company should pay, calculating risk margin for lapse is a key issue in the VA business. In this study, risk margin for VA lapses is estimated with Wang transform suggested by Wang (2000, 2002).

The purpose of this paper is the coupled nonlinear fractal Schrödinger system is defined by using fractal derivative, and its variational principle is constructed by the fractal semi-inverse method. The approximate analytical solution of the coupled nonlinear fractal Schrödinger system is obtained by the fractal variational iteration transform method based on the proposed variational theory and fractal two-scales transform method. Finally, an example illustrates the proposed method is efficient to deal with complex nonlinear fractal systems.

The coupled nonlinear fractal Schrödinger system is described by using the fractal derivative, and its fractal variational principle is obtained by the fractal semi-inverse method. A novel approach is proposed to solve the fractal model based on the variational theory.

The fractal variational iteration transform method is an excellent method to solve the fractal differential equation system.

The author first presents the fractal variational iteration transform method to find the approximate analytical solution for fractal differential equation system. The example illustrates the accuracy and efficiency of the proposed approach.

This study aims to reveal the essential characteristics of nonstationary signals and explore the high-concentration representation in the joint time–frequency (TF) plane.

In this paper, the authors consider the effective TF analysis for nonstationary signals consisting of multiple components.

To make it, the authors propose the combined multi-window Gabor transform (CMGT) under the scheme of multi-window Gabor transform by introducing the combination operator. The authors establish the completeness utilizing the discrete piecewise Zak transform and provide the perfect-reconstruction conditions with respect to combined TF coefficients. The high-concentration is achieved by optimization. The authors establish the optimization function with considerations of TF concentration and computational complexity. Based on Bergman formulation, the iteration process is further analyzed to obtain the optimal solution.

With numerical experiments, it is verified that the proposed CMGT performs better in TF analysis for multi-component nonstationary signals.

Adopting aspects of the resource-based perspective and interorganizational relational dynamics, this paper examines the notion of resource transformation in the reconstitution of broken interorganizational relationships.

Following a qualitative approach, the research involved four in-depth case studies of buyer–supplier relationships among 12 Scandinavian manufacturing firms.

The results suggest that reconstituting broken interorganizational relationships, whether overlooked or underutilized, can pose important consequences for resource transformations. To adapt in dynamic environments, firms use resources in new combinations, and various relationship-specific resources may be difficult, if not impossible, to transform independent of the reconstitution process. Such resource transformations can occur when competencies in reconstituting interorganizational relationships are combined to synthesize novel resources or recombined with other resources. Four identified types of resource transformations in reconstitution processes – in production facilities, products, human know-how and coordination of interorganizational collaboration – can occur in each firm and/or in the interorganizational relationship.

Although the explorative multiple-case study approach afforded novel insights, the findings have no representative or generalizable implications in any positivist sense and thus warrant careful interpretation. Nevertheless, they make important contributions to the literature and illuminate promising avenues for future research, which should involve additional data collection and quantitative studies.

As firms reconstitute broken interorganizational relationships, the transformation of their resources can provide new, expected resources capable of generating substantial benefits.

This paper fills an identified gap in research regarding how reconstituting broken interorganizational relationships influence the transformation of resources. The paper provides new conceptual and empirical insights as well as makes several contributions to the literature on the topic.

The purpose of this paper is to describe the Lane–Emden equation by the fractal derivative and establish its variational principle by using the semi-inverse method. The variational principle is helpful to research the structure of the solution. The approximate analytical solution of the fractal Lane–Emden equation is obtained by the variational iteration method. The example illustrates that the suggested scheme is efficient and accurate for fractal models.

The author establishes the variational principle for fractal Lane–Emden equation, and its approximate analytical solution is obtained by the variational iteration method.

The variational iteration method is very fascinating in solving fractal differential equation.

The author first proposes the variational iteration method for solving fractal differential equation. The example shows the efficiency and accuracy of the proposed method. The variational iteration method is valid for other nonlinear fractal models as well.

This study aims to perform the experimental work on a laboratory-constructed steel truss bridge model on which hammer blows are applied for excitation. The vibration response signals of the bridge structure are collected using sensors placed at different nodes. The different damaged states such as no damage, single damage, double damage and triple damage are introduced by cutting members of the bridge. The masked noise with recorded vibration responses generates challenge to properly analyze the health of bridge structure.

The analytical modal properties are obtained from finite element model (FEM) developed using SAP2000 software. The response signals are analyzed in frequency domain by power spectrum and in time-frequency domain using spectrogram and Stockwell transform. Various low pass signal-filtering techniques such as variational filter, lowpass sparse banded (AB) filter and Savitzky–Golay (SG) differentiator filter are also applied to refine vibration signals. The proposed methodology further comprises application of Hilbert transform in combination with MUSIC and ESPRIT techniques.

The outcomes of SG filter provided the denoised signals using appropriate polynomial degree with proper selected window length. However, certain unwanted frequency peaks still appeared in the outcomes of SG filter. The SG-filtered signals are further analyzed using fused methodology of Hilbert transform-ESPRIT, which shows high accuracy in identifying modal frequencies at different states of the steel truss bridge.

The sequence of proposed methodology for denoising vibration response signals using SG filter with Hilbert transform-ESPRIT is a novel approach. The outcomes of proposed methodology are much refined and take less computational time.

The purpose of this paper is to study the new (3 + 1)-dimensional integrable fourth-order nonlinear equation which is used to model the shallow water waves.

By means of the Cole–Hopf transform, the bilinear form of the studied equation is extracted. Then the ansatz function method combined with the symbolic computation is implemented to construct the breather, multiwave and the interaction wave solutions. In addition, the subequation method tis also used to search for the diverse travelling wave solutions.

The breather, multiwave and the interaction wave solutions and other wave solutions like the singular periodic wave structure and dark wave structure are obtained. To the author’s knowledge, the solutions obtained are all new and have never been reported before.

The solutions obtained in this work have never appeared in other literature and can be regarded as an extension of the solutions for the new (3 + 1)-dimensional integrable fourth-order nonlinear equation.

The purpose of this paper is to develop a model to hedge annuity portfolios against increases in life expectancy. Across the globe, and in the industrial nations in particular, people have seen an unprecedented increase in their life expectancy over the past decades. The benefits of this apply to the individual, but the dangers apply to annuity providers. Insurance companies often possess no effective tools to address the longevity risk inherent in their annuity portfolio. Securitization can serve as a substitute for classic reinsurance, as it also transfers risk to third parties.

This paper extends on methods insurer's can use to hedge their annuity portfolio against longevity risk with the help of annuity securitization. Future mortality rates with the Lee-Carter-model and use the Wang-transformation to incorporate insurance risk are forecasted. Based on the percentile tranching method, where individual tranches are aligned to Standard & Poor's ratings, we price an inverse survivor bond. This bond offers fix coupon payments to investors, while the principal payments are at risk and depend on the survival rate within the underlying portfolio.

The contribution to the academic literature is threefold. On the theoretical side, building on the work of Kim and Choi (2011), we adapt their pricing model to the current market situation. Putting the principal at risk instead of the coupon payments, the insurer is supplied with sufficient capital to cover additional costs due to longevity. On the empirical side, the method for the German market is specified. Inserting specific country data into the model, price sensitivities of the presented securitization model are analyzed. Finally, in a case study, the procedure to the annuity portfolio of a large German life insurer is applied and the price of hedging longevity risk is calculated.

To illustrate the implication of this bond structure, several sensitivity tests were conducted before applying the pricing model to the retail sample annuity portfolio from a leading German life insurer. The securitization structure was applied to calculate the securitization prices for a sample portfolio from a large life insurance company.

The findings contribute to the current discussion about how insurers can face longevity risk within their annuity portfolios. The fact that the rating structure has such a severe impact on the overall hedging costs for the insurer implies that companies that are willing to undergo an annuity securitization should consider their deal structure very carefully. In addition, we have pointed out that in imperfect markets, the retention of the equity tranche by the originator might be advantageous. Nevertheless, one has to bear in mind that by this behavior, the insurer is able to reduce the overall default risk in his balance sheet by securitizing a life insurance portfolio; however, the fraction of first loss pieces from defaults increases more than proportionally. The insurer has to take care to not be left with large, unwanted remaining risk positions in his books.

In this paper, we extend on methods insurer's can use to hedge their annuity portfolio against longevity risk with the help of annuity securitization. To do so, we take the perspective of the issuing insurance company and calculate the costs of hedging in a four-step process. On the theoretical side, building on the work of Kim and Choi (2011), we adapt their pricing model to the current market situation. On the empirical side, we specify the method for the German market. Inserting specific country data into the model, price sensitivities of the presented securitization model are analyzed.

A semiparametric stochastic frontier model is proposed for panel data, incorporating several flexible features. First, a constant elasticity of substitution (CES) production frontier is considered without log-transformation to prevent induced non-negligible estimation bias. Second, the model flexibility is improved via semiparameterization, where the technology is an unknown function of a set of environment variables. The technology function accounts for latent heterogeneity across individual units, which can be freely correlated with inputs, environment variables, and/or inefficiency determinants. Furthermore, the technology function incorporates a single-index structure to circumvent the curse of dimensionality. Third, distributional assumptions are eschewed on both stochastic noise and inefficiency for model identification. Instead, only the conditional mean of the inefficiency is assumed, which depends on related determinants with a wide range of choice, via a positive parametric function. As a result, technical efficiency is constructed without relying on an assumed distribution on composite error. The model provides flexible structures on both the production frontier and inefficiency, thereby alleviating the risk of model misspecification in production and efficiency analysis. The estimator involves a series based nonlinear least squares estimation for the unknown parameters and a kernel based local estimation for the technology function. Promising finite-sample performance is demonstrated through simulations, and the model is applied to investigate productive efficiency among OECD countries from 1970–2019.