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The purpose of this paper is to study large deviations for the solution processes of a stochastic equation incorporated with the effects of nonlocal condition.

A weak convergence approach is adopted to establish the Laplace principle, which is same as the large deviation principle in a Polish space. The sufficient condition for any family of solutions to satisfy the Laplace principle formulated by Budhiraja and Dupuis is used in this work.

Freidlin–Wentzell type large deviation principle holds good for the solution processes of the stochastic functional integral equation with nonlocal condition.

The asymptotic exponential decay rate of the solution processes of the considered equation towards its deterministic counterpart can be estimated using the established results.

The current paper proposes a prediction model for a cryptocurrency that encompasses three properties observed in the markets for cryptocurrencies—namely high volatility, illiquidity, and regime shifts. As far as the authors’ knowledge extends, this paper is the first attempt to introduce a stochastic differential equation (SDE) for pricing cryptocurrencies while explicitly integrating the mentioned three significant stylized facts.

Cryptocurrencies are increasingly utilized by investors and financial institutions worldwide as an alternative means of exchange. To the authors’ best knowledge, there is no SDE in the literature that can be used for representing and evaluating the data-generating process for the price of a cryptocurrency.

By using Ito calculus, the authors provide a solution for the suggested SDE along with mathematical proof. Numerical simulations are performed and compared to the real data, which seems to capture the dynamics of the price path of two main cryptocurrencies in the real markets.

The stochastic differential model that is introduced and solved in this article is expected to be useful for the pricing of cryptocurrencies in situations of high volatility combined with structural changes and illiquidity. These attributes are apparent in the real markets for cryptocurrencies; therefore, accounting explicitly for these underlying characteristics is a necessary condition for accurate evaluation of cryptocurrencies.

This survey explores the application of real options theory to the field of health economics. The integration of options theory offers a valuable framework to address these challenges, providing insights into healthcare investments, policy analysis and patient care pathways.

This research employs the real options theory, a financial concept, to delve into health economics challenges. Through a systematic approach, three distinct models rooted in this theory are crafted and analyzed. Firstly, the study examines the value of investing in emerging health technology, factoring in future advantages, associated costs and unpredictability. The second model is patient-centric, evaluating the choice between immediate treatment switch and waiting for more clarity, while also weighing the associated risks. Lastly, the research assesses pandemic-related government policies, emphasizing the importance of delaying decisions in the face of uncertainties, thereby promoting data-driven policymaking.

Three different real options models are presented in this study to illustrate their applicability and value in aiding decision-makers. (1) The first evaluates investments in new technology, analyzing future benefits, discount rates and benefit volatility to determine investment value. (2) In the second model, a patient has the option of switching treatments now or waiting for more information before optimally switching treatments. However, waiting has its risks, such as disease progression. By modeling the potential benefits and risks of both options, and factoring in the time value, this model aids doctors and patients in making informed decisions based on a quantified assessment of potential outcomes. (3) The third model concerns pandemic policy: governments can end or prolong lockdowns. While awaiting more data on the virus might lead to economic and societal strain, the model emphasizes the economic value of deferring decisions under uncertainty.

This research provides a quantified perspective on various decisions in healthcare, from investments in new technology to treatment choices for patients to government decisions regarding pandemics. By applying real options theory, stakeholders can make more evidence-driven decisions.

Decisions about patient care pathways and pandemic policies have direct societal implications. For instance, choices regarding the prolongation or ending of lockdowns can lead to economic and societal strain.

The originality of this study lies in its application of real options theory, a concept from finance, to the realm of health economics, offering novel insights and analytical tools for decision-makers in the healthcare sector.

This study aims to predict overnight stays in Italy at tourist accommodation facilities through a nonlinear, single factor, stochastic model called CIR#. The contribution of this study is twofold: in terms of forecast accuracy and in terms of parsimony (both from the perspective of the data and the complexity of the modeling), especially when a regular pattern in the time series is disrupted. This study shows that the CIR# not only performs better than the considered baseline models but also has a much lower error than other additional models or approaches reported in the literature.

Typically, tourism demand tends to follow regular trends, such as low and high seasons on a quarterly/monthly level and weekends and holidays on a daily level. The data set consists of nights spent in Italy at tourist accommodation establishments as collected on a monthly basis by Eurostat before and during the COVID-19 pandemic breaking regular patterns.

Traditional tourism demand forecasting models may face challenges when massive amounts of search intensity indices are adopted as tourism demand indicators. In addition, given the importance of accurate forecasts, many studies have proposed novel hybrid models or used various combinations of methods. Thus, although there are clear benefits in adopting more complex approaches, the risk is that of dealing with unwieldy models. To demonstrate how this approach can be fruitfully extended to tourism, the accuracy of the CIR# is tested by using standard metrics such as root mean squared errors, mean absolute errors, mean absolute percentage error or average relative mean squared error.

The CIR# model is notably simpler than other models found in literature and does not rely on black box techniques such as those used in neural network (NN) or data science-based models. The carried analysis suggests that the CIR# model outperforms other reference predictions in terms of statistical significance of the error.

The proposed model stands out for being a viable option to the Holt–Winters (HW) model, particularly when dealing with irregular data.

The proposed model has demonstrated superiority even when compared to other models in the literature, and it can be especially useful for tourism stakeholders when making decisions in the presence of disruptions in data patterns.

The novelty lies in the fact that the proposed model is a valid alternative to the HW, especially when the data are not regular. In addition, compared to many existing models in the literature, the CIR# model is notably simpler and more transparent, avoiding the “black box” nature of NN and data science-based models.

一般来说, 旅游需求往往遵循规律的趋势, 例如季度/月的淡季和旺季, 以及日常的周末和假期。该数据集包括欧盟统计局在打破常规模式的2019冠状病毒病大流行之前和期间每月收集的在意大利旅游住宿设施度过的夜晚。

本研究旨在通过一个名为cir#的非线性单因素随机模型来预测意大利游客住宿设施的过夜住宿情况。这项研究的贡献是双重的:在预测准确性方面和在简洁方面(从数据和建模复杂性的角度来看), 特别是当时间序列中的规则模式被打乱时。我们表明, cir#不仅比考虑的基线模型表现更好, 而且比文献中报告的其他模型或方法具有更低的误差。

当大量搜索强度指标被作为旅游需求指标时, 传统的旅游需求预测模型将面临挑战。此外, 鉴于准确预测的重要性, 许多研究提出了新的混合模型或使用各种方法的组合。因此, 尽管采用更复杂的方法有明显的好处, 但风险在于处理难使用的模型。为了证明这种方法能有效地扩展到旅游业, 使用RMSE、MAE、MAPE或AvgReIMSE等标准指标来测试cir#的准确性。

cir#模型明显比文献中发现的其他模型简单, 并且不依赖于黑盒技术, 例如在神经网络或基于数据科学的模型中使用的技术。所进行的分析表明, cir#模型在误差的统计显著性方面优于其他参考预测。

这个模型作为Holt-Winters模型的一个拟议模型, 特别是在处理不规则数据时。

即使与文献中的其他模型相比, 所提出的模型也显示出优越性, 并且在数据模式中断时对旅游利益相关者做出决策特别有用。

创新之处在于所提出的模型是Holt-Winters模型的有效替代方案, 特别是当数据不规律时。此外, 与文献中的许多现有模型相比, cir#模型明显更简单、更透明, 避免了神经网络和基于数据科学的模型的“黑箱”性质。

Normalmente, la demanda turística tiende a seguir tendencias regulares, como temporadas altas y bajas a nivel trimestral/mensual y fines de semana y festivos a nivel diario. El conjunto de datos consiste en las pernoctaciones en Italia en establecimientos de alojamiento turístico recogidas mensualmente por Eurostat antes y durante la pandemia de COVID-19, rompiendo los patrones regulares.

El presente estudio pretende predecir las pernoctaciones en Italia en establecimientos de alojamiento turístico mediante un modelo estocástico no lineal de un solo factor denominado CIR#. La contribución de este estudio es doble: en términos de precisión de la predicción y en términos de parsimonia (tanto desde la perspectiva de los datos como de la complejidad de la modelización), especialmente cuando un patrón regular en la serie temporal se ve interrumpido. Demostramos que el CIR# no sólo aplica mejor que los modelos de referencia considerados, sino que también tiene un error mucho menor que otros modelos o enfoques adicionales de los que se informa en la literatura.

Los modelos tradicionales de previsión de la demanda turística pueden enfrentarse a desafíos cuando se adoptan cantidades masivas de índices de intensidad de búsqueda como indicadores de la demanda turística. Además, dada la importancia de unas previsiones precisas, muchos estudios han propuesto modelos híbridos novedosos o han utilizado diversas combinaciones de métodos. Así pues, aunque la adopción de enfoques más complejos presenta ventajas evidentes, el riesgo es el de enfrentarse a modelos poco manejables. Para demostrar cómo este enfoque puede extenderse de forma fructífera al turismo, se comprueba la precisión del CIR# utilizando métricas estándar como RMSE, MAE, MAPE o AvgReIMSE.

El modelo CIR# es notablemente más sencillo que otros modelos encontrados en la literatura y no se basa en técnicas de caja negra como las utilizadas en los modelos basados en redes neuronales o en la ciencia de datos. El análisis realizado sugiere que el modelo CIR# supera a otras predicciones de referencia en términos de significación estadística del error.

El modelo propuesto destaca por ser una opción viable al modelo Holt-Winters, sobre todo cuando se trata de datos irregulares.

El modelo propuesto ha demostrado su superioridad incluso cuando se compara con otros modelos de la bibliografía, y puede ser especialmente útil para los agentes del sector turístico a la hora de tomar decisiones cuando se producen alteraciones en los patrones de datos.

La novedad radica en que el modelo propuesto es una alternativa válida al Holt-Winters especialmente cuando los datos no son regulares. Además, en comparación con muchos modelos existentes en la literatura, el modelo CIR# es notablemente más sencillo y transparente, evitando la naturaleza de “caja negra” de los modelos basados en redes neuronales y en ciencia de datos.

The purpose of this study is to present a general review that provides an overview of the concept of sustainability and the effectiveness of mathematics curricula in courses where deeper work on economic and environmental sustainability has become central.

A qualitative methodology consisting of a review based on a pre-defined systematic method was used to exhaustively search and identify the most relevant answers to the research question: What is the role of mathematics to sustainability? To facilitate answering such a broad question, several concrete questions were formulated. Answers from published and unpublished documents were analysed. The quality of the extracted data was assessed, and the results were synthesized.

It was concluded that, on the one hand, the discipline of mathematics has much to contribute to solving the problems of sustainability; on the other hand, new mathematics is appearing stimulated by new challenges.

This work presents social implications in an innovative way. It allows for an increase in educational sustainability by bringing the academic community closer to the business world and the challenges of society and, furthermore, by having a major impact on the motivation of teachers and students to develop cooperative work within university institutions.

The originality is based on an a priori analysis for the construction and implementation of didactic tools for university teacher training in the area of mathematics within the framework of sustainable development, both economically and environmentally.

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.

Due to the cross-network effect, two-sided users communicate with each other, producing a coupling network. To study the spread of platform self-operation in two-sided users' marketing and purchasing tactics, this paper considers the differences in reputation acquired by platform-owned and third-party operating channels.

This study proposes a two-layer network with cross-network links: one layer represents the social network of consumers, while the other layer represents the competitive network of buyers. A closed system of differential equations, based on the binary dynamics of the stochastic network, is developed to study the trend and stability points of the platform self-operation dissemination. Then the overall benefits of platform are analyzed to unify the platform diffusion and pricing strategies.

The degree of difference in social influence and cross-network effects affect diffusion synergistically. Cross-network effects hinder diffusion when there is a significant difference of social influence between consumers and sellers but promote diffusion when there is little difference of social influence between consumers and sellers. Additionally, the network weights and reputation gap exhibit a nonlinear correlation with diffusion. For pricing strategy of the platform, it can achieve maximum profit when the pricing of self-operated goods and third-party-operated goods is equal.

This study considers the complex network architecture created by bilateral markets and the dynamic influence of group interactions on product. Additionally, this study takes reputation into account when considering the price and dissemination tactics of various operating channels, offering guidelines for platforms to control merchants and mediate disputes between various operating channels.

The purpose of this paper is to improve autonomous flight performance of a fixed-wing unmanned aerial vehicle (UAV) via simultaneous morphing wingtip and control system design conducted with optimization, computational fluid dynamics (CFD) and machine learning approaches.

The main wing of the UAV is redesigned with morphing wingtips capable of dihedral angle alteration by means of folding. Aircraft dynamic model is derived as equations depending only on wingtip dihedral angle via Nonlinear Least Squares regression machine learning algorithm. Data for the regression analyses are obtained by numerical (i.e. CFD) and analytical approaches. Simultaneous perturbation stochastic approximation (SPSA) is incorporated into the design process to determine the optimal wingtip dihedral angle and proportional-integral-derivative (PID) coefficients of the control system that maximizes autonomous flight performance. The performance is defined in terms of trajectory tracking quality parameters of rise time, settling time and overshoot. Obtained optimal design parameters are applied in flight simulations to test both longitudinal and lateral reference trajectory tracking.

Longitudinal and lateral autonomous flight performances of the UAV are improved by redesigning the main wing with morphing wingtips and simultaneous estimation of PID coefficients and wingtip dihedral angle with SPSA optimization.

This paper originally discusses the simultaneous design of innovative morphing wingtip and UAV flight control system for autonomous flight performance improvement. The proposed simultaneous design idea is conducted with the SPSA optimization and a machine learning algorithm as a novel approach.

This study aims to discuss climate change, by modifying the timing of several agricultural operations, reduce the efficiency and yield of inputs leading to a lower production level. The reduction of the effects of climate change on production yields and on farmers' technical efficiency (TE) requires the adoption of adaptation strategies. This paper analyses the impact of climate change adaptation strategies adopted on maize farmers' TE in Benin.

This paper uses an endogeneity-corrected stochastic production frontier approach based on data randomly collected from 354 farmers located in three different agro-ecological zones of Benin.

Estimation results revealed that the adoption of adaptation strategies improve maize farmers' TE by 1.28%. Therefore, polices to improve farmers' access to climate change adaptation strategies are necessarily for the improvement of farmers' TE and yield.

The results of this study contribute to the policy debate on the enhancement of food security by increasing farmers' TE through easy access to climate change adaptation strategies. The improvement of farmers' TE will in turn improve the livelihoods of the communities and therefore contribute to the achievement of Sustainable Development Goals 1, 2 and 13.

This study contributes to theoretical and empirical debate on the relationship between adaptation to climate change and farmers' TE. It also adapts a new methodology (endogeneity-corrected stochastic production frontier approach) to correct the endogeneity problem due to the farmers' adaptation decision.

The current analysis produces the fractional sample of non-Newtonian Casson and Williamson boundary layer flow considering the heat flux and the slip velocity. An extended sheet with a nonuniform thickness causes the steady boundary layer flow’s temperature and velocity fields. Our purpose in this research is to use Akbari Ganji method (AGM) to solve equations and compare the accuracy of this method with the spectral collocation method.

The trial polynomials that will be utilized to carry out the AGM are then used to solve the nonlinear governing system of the PDEs, which has been transformed into a nonlinear collection of linked ODEs.

The profile of temperature and dimensionless velocity for different parameters were displayed graphically. Also, the effect of two different parameters simultaneously on the temperature is displayed in three dimensions. The results demonstrate that the skin-friction coefficient rises with growing magnetic numbers, whereas the Casson and the local Williamson parameters show reverse manners.

Moreover, the usefulness and precision of the presented approach are pleasing, as can be seen by comparing the results with previous research. Also, the calculated solutions utilizing the provided procedure were physically sufficient and precise.