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In this paper we talk about complex matrix quaternions (biquaternions) and we deal with some abstract methods in mathematical complex matrix analysis.

We introduce and investigate the complex space HC consisting of all 2 × 2 complex matrices of the form ξ=z1+iw1z2+iw2−z‾2−iw‾2z‾1+iw‾1, (z1,w1,z2,w2)∈C4.

We develop on HC a new matrix holomorphic structure for which we provide the fundamental operational calculus properties.

We give sufficient and necessary conditions in terms of Cauchy–Riemann type quaternionic differential equations for holomorphicity of a function of one complex matrix variable ξ∈HC. In particular, we show that we have a lot of holomorphic functions of one matrix quaternion variable.

Using the next-day and next-week returns of stocks in the Korean market, we examine the association of option volume ratios – i.e. the option-to-stock (O/S) ratio, which is the total volume of put options and call options scaled by total underlying equity volume, and the put-call (P/C) ratio, which is the put volume scaled by total put and call volume – with future returns. We find that O/S ratios are positively related to future returns, but P/C ratios have no significant association with returns. We calculate individual, institutional, and foreign investors’ option ratios to determine which ratios are significantly related to future returns and find that, for all investors, higher O/S ratios predict higher future returns. The predictability of P/C depends on the investors: institutional and individual investors’ P/C ratios are not related to returns, but foreign P/C predicts negative next-day returns. For net-buying O/S ratios, institutional net-buying put-to-stock ratios consistently predict negative future returns. Institutions’ buying and selling put ratios also predict returns. In short, institutional put-to-share ratios predict future returns when we use various option ratios, but individual option ratios do not.

Our result of this paper aims to indicate that the beta pricing formula could be applied in a long-term model setting as well.

In this paper, we show that the capital asset pricing model can be derived from a three-period general equilibrium model.

We show that our extended model yields a Pareto efficient outcome.

The capital asset pricing model (CAPM) model can be used for pricing long-lived assets.

Long-term modelling and sustainability can be modelled in our setting.

Our results were only known for two periods. The extension to 3 periods opens up a large scope of applicational possibilities in asset pricing, behavioural analysis and long-term efficiency.

The promotion of autonomous vehicles introduces privacy and security risks, underscoring the pressing need for responsible innovation implementation. To more effectively address the societal risks posed by autonomous vehicles, considering collaborative engagement of key stakeholders is essential. This study aims to provide insights into the governance of potential privacy and security issues in the innovation of autonomous driving technology by analyzing the micro-level decision-making processes of various stakeholders.

For this study, the authors use a nuanced approach, integrating key stakeholder theory, perceived value theory and prospect theory. The study constructs a model based on evolutionary game for the privacy and security governance mechanism of autonomous vehicles, involving enterprises, governments and consumers.

The governance of privacy and security in autonomous driving technology is influenced by key stakeholders’ decision-making behaviors and pivotal factors such as perceived value factors. The study finds that the governmental is influenced to a lesser extent by the decisions of other stakeholders, and factors such as risk preference coefficient, which contribute to perceived value, have a more significant influence than appearance factors like participation costs.

This study lacks an investigation into the risk sensitivity of various stakeholders in different scenarios.

The study delineates the roles and behaviors of key stakeholders and contributes valuable insights toward addressing pertinent risk concerns within the governance of autonomous vehicles. Through the study, the practical application of Responsible Innovation theory has been enriched, addressing the shortcomings in the analysis of micro-level processes within the framework of evolutionary game.

The framework of this paper is financial mathematics and, more specifically, the control of data fraud and manipulation with their subsequent economic effects, namely, in financial markets. The purpose of this paper is to calculate the global loss or gain, which supposes, for the borrower, a change of the interest rate while the contracted loan is in force or, in another case, the loan has finished.

The methodology used in this work has been, in the first place, a review of the existing literature on the topic of manipulability and abusiveness of the loan interest rates applied by banks; in the second place, the introduction of a mathematical-financial analysis to calculate the interests paid in excess; and, finally, the compilation of several sentences issued on the application of the so-called mortgage loan reference index (MLRI) to mortgage loans in Spain.

There are three main contributions in this paper. First, the calculation of the interests paid in excess in the amortization of mortgage loans referenced to an overvalued interest rate. Second, an empirical application shows the amount to be refunded to a Spanish consumer when amortizing his/her mortgage loan referenced to the MLRI instead of the Euro InterBank Offered Rate (EURIBOR). Third, consideration has been made to the effects and the possible solutions to the legal problems arising from this type of contract.

This research is a useful tool capable of implementing the financial calculation needed to find out overpaid interests in mortgage loans and to execute the sentences dealing with this topic. However, a limitation of this study is the lack of enough sentences on mortgage loans referenced to the MLRI to get some additional information about the number of borrowers affected by these legal sentences and the amount refunded by the financial institutions.

To the best of the authors’ knowledge, this is the first time that deviations in the payment of interests have been calculated when amortizing a mortgage.

This study aims to explore the relationship between chief executive officer (CEO) power and stock price crash risk in India. Furthermore, it seeks to analyse how insider trades may moderate the impact of CEO power on stock price crash risk.

A study of 236 companies from the S&P BSE 500 Index (2014–2023) have been analysed through pooled ordinary least square (OLS) regression in the baseline analysis. To enhance the results' reliability, robustness checks include alternative methodologies, such as panel data regression with fixed-effects, binary logistic regression and Bayesian regression. Additional control variables and alternative crash risk measure have also been utilised. To address potential endogeneity, instrumental variable techniques such as two-stage least squares (IV-2SLS) and difference-in-difference (DiD) methodologies are utilised.

Stakeholder theory is supported by results revealing that CEO power proxies like CEO duality, status and directorship reduce one-year ahead stock price crash risk and vice versa. Insider trades are found to moderate the link between select dimensions of CEO power and stock price crash risk. These findings persist after addressing potential endogeneity concerns, and the results remain consistent across alternative methodologies and variable inclusions.

This study significantly advances research on stock price crash risk, especially in emerging economies like India. The implications of these findings are crucial for investors aiming to mitigate crash risk, for corporations seeking enhanced governance measures and for policymakers considering the economic and welfare consequences associated with this phenomenon.

Based on relationship marketing theory, this study aims to test the effect of social customer relationship management (social CRM) on customer satisfaction (CS) and loyalty (CL).

To assess the proposed framework, structural equation modeling was performed on the data of 314 automotive customers surveyed online.

Social CRM dimensions [traditional CRM (TCRM) and social media (SM) technology use] have a direct and positive effect on CS. On the other hand, only TCRM has a direct and significant influence on CL, while the SM technology use effect seems to be indirect rather than direct. Indeed, the findings have provided empirical support for the contention that CS plays a mediating role between social CRM dimensions and CL.

In the automotive sector and developing countries in particular, companies’ managers could increase CS and CL and consequently enhance their competitiveness and market share by adopting an effective social CRM strategy. From this perspective, companies should focus their social CRM campaigns on the most SM used by customers, offer personalized choices and improve customer experience, interaction and value co-creation.

This paper enriches the understanding of how social CRM can affect CS and CL. The scales of social CRM, CS and CL were validated in the context of developing countries and the automotive sector. Furthermore, the direct and mediating effect of CS between social CRM (TCRM and SM) and CL was also confirmed.

Basándose en la teoría del marketing relacional, este estudio pretende comprobar el efecto de la gestión social de las relaciones con los clientes (CRM social) sobre la satisfacción y la fidelidad de los clientes.

Para evaluar el marco propuesto, se realizó un modelado de ecuaciones estructurales sobre los datos de 314 clientes de automoción encuestados online.

Las dimensiones del CRM social (CRM tradicional y uso de tecnología de medios sociales) tienen un efecto directo y positivo en la satisfacción del cliente. Por otro lado, solamente el CRM tradicional tiene una influencia directa y significativa en la fidelidad del cliente, mientras que el efecto del uso de la tecnología de medios sociales parece ser más indirecto que directo. De hecho, los resultados han proporcionado apoyo empírico a la afirmación de que la satisfacción del cliente desempeña un papel mediador entre las dimensiones del CRM social y la fidelidad del cliente.

Este artículo enriquece la comprensión de cómo el CRM social puede afectar a la satisfacción y la fidelidad de los clientes. Las escalas de CRM social, satisfacción del cliente y fidelidad del cliente se validaron en el contexto de países en vías de desarrollo y del sector automovilístico. Además, también se confirmó el efecto directo y mediador de la satisfacción del cliente entre el CRM social (CRM tradicional y medios sociales) y la fidelidad del cliente.

En el sector de la automoción y en los países en desarrollo en particular, los directivos de las empresas podrían aumentar la satisfacción y fidelidad de sus clientes y, en consecuencia, mejorar su competitividad y cuota de mercado adoptando una estrategia eficaz de CRM social. Desde esta perspectiva, las empresas deberían centrar sus campañas de CRM social en los medios más utilizados por los clientes, ofrecer opciones personalizadas y mejorar la experiencia del cliente, la interacción y la cocreación de valor.

基于关系营销理论, 本研究旨在检验社会化客户关系管理（social CRM）对客户满意度和忠诚度的影响。

为评估所提出的框架, 对 314 名汽车客户的在线调查数据进行了结构方程建模。

社交客户关系管理维度（传统客户关系管理和社交媒体技术使用）对客户满意度有直接的积极影响。另一方面, 只有传统客户关系管理对客户忠诚度有直接和显著的影响, 而社交媒体技术使用的影响似乎是间接而非直接的。事实上, 研究结果为客户满意度在社交客户关系管理维度和客户忠诚度之间发挥中介作用的论点提供了实证支持。

本文丰富了人们对社交客户关系管理如何影响客户满意度和忠诚度的认识。本文以发展中国家和汽车行业为背景, 对社会化客户关系管理、客户满意度和客户忠诚度的量表进行了验证。此外, 还证实了客户满意度在社会化客户关系管理（传统客户关系管理和社会化媒体）与客户忠诚度之间的直接和中介效应。

尤其是发展中国家, 企业管理者可以通过采取有效的社交客户关系管理战略, 提高客户满意度和忠诚度, 进而增强竞争力和市场份额。从这个角度来看, 企业应将社交客户关系管理活动的重点放在客户使用最多的社交媒体上, 提供个性化选择, 改善客户体验、互动和价值共创。

In many real-life situations ranging from financial to volcanic data, growth is described either by a power law – which is linear in log-log scale or by a quadratic dependence in the log-log scale. The purpose of this paper is to explain this empirical fact.

The authors use natural scale invariance requirements.

In this paper, the authors used natural scale invariance requirement to explain the ubiquity of quadratic log-log dependencies. The authors also explain what to do if quadratic log-log models turn out to be insufficiently accurate. In this case, scale-invariance requirements lead to dependencies which in the log-log scale take cubic, 4th order, etc. form.

To the best of authors’ knowledge, this is the first theoretical explanation of the empirical quadratic log-log dependence.

The authors explore the hypothesis that some movements in commodity prices are anticipated (news shocks) and can trigger aggregate fluctuations in small open emerging economies. This paper aims to discuss the aforementioned objective.

The authors build a multi-sector dynamic stochastic general equilibrium model with endogenous commodity production. There are five exogenous processes: a country-specific interest rate shock that responds to commodity price fluctuations, a productivity (TFP) shock for each sector and a commodity price shock. Both TFP and commodity price shocks are composed of unanticipated and anticipated components.

The authors show that news shocks to commodity prices lead to higher output, investment and consumption, and a countercyclical movement in the trade-balance-to-output ratio. The authors also show that commodity price news shocks explain about 24% of output aggregate fluctuations in the small open economy.

Given the importance of both anticipated and unanticipated commodity price shocks, policymakers should pay attention to developments in commodity markets when designing policies to attenuate the business cycles. Future research should investigate the design of optimal fiscal and monetary policies in SOE subject to news shocks in commodity prices.

This paper contributes to the knowledge of the sources of fluctuations in emerging economies highlighting the importance of a new source: news shocks in commodity prices.

The authors characterize the conditions under which a country may eventually split and when it splits within an infinite horizon multi-stage differential game.

In contrast to the existing literature, the authors do not assume that after splitting, players will adopt Markovian strategies. Instead, the authors assume that while the splitting country plays Markovian, the remaining coalition remains committed to the collective control of pollution and plays open-loop.

Within a full linear-quadratic model, the authors characterize the optimal strategies. The authors later compare with the outcomes of the case where the splitting country and the remaining coalition play both Markovian. The authors highlight several interesting results in terms of the implications for long-term pollution levels and the duration of coalitions under heterogenous strategies as compared to Markovian behavior.

In this paper, the authors have illustrated the richness of the simplications of enlarging the set of strategies in terms of the emergence of coalitions, their duration and the implied welfare levels per player. Varying only three parameters (the technological gap, pollution damage and coalition payoff share distribution across players), the authors have been able to generate, among other findings, quite different rankings of welfare per player depending on whether the remaining coalitions after split play Markovian or stay precommited to the pre-splitting period decisions.