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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.

This paper investigates the relationship between climate finance and climate ergodicity. More specifically the paper examines how climate ergodicity as measured by a mean-reverting Ornstein–Uhlenbeck process affects the value of climate-linked bonds.

Bond valuation is evaluated using Monte Carlo methods of the Ornstein–Uhlenbeck process. The paper describes climate risk in terms of the Hurst coefficient and derives a direct linkage between the Ornstein–Uhlenbeck process and the Hurst measure.

We use the Ornstein–Uhlenbeck mean reversion relationship in its OLS form to estimate Hurst coefficients for 5 × 5° grids across the US for monthly temperature and precipitation. We find that the ergodic property holds with Hurst coefficients between 0.025 and 0.01 which implies increases in climate standard deviation in the range of 25%–50%.

The approach provides a means to stress-test the bond prices to uncover the probability distribution about the issue value of bonds. The methods can be used to price or stress-test bonds issued by firms in climate sensitive industries. This will be of particular interest to the Farm Credit System and the Farm Credit Funding Corporation with agricultural loan portfolios subject to spatial climate risks.

This paper examines bond issues under conditions of rising climate risks using Hurst coefficients derived from an Ornstein–Uhlenbeck process.

Marketplace lending has substantially changed since the first peer-to-peer lending platforms emerged in 2006. The industry is now an alternative to bank lending, predicted to total $70 billion for consumer and business loans worldwide by 2030. Marketplace lending is often deemed less safe than bank loans, mainly due to these portfolios' high degree of hidden information. These include needing more information on borrowers and potential correlations between them, which might lead to higher risk than is apparent at first glance. Deterministic processes cannot capture tail risk appropriately, so platforms and lenders should employ stochastic processes. This chapter introduces a Monte Carlo simulation and machine learning (ML) process to evaluate and monitor portfolios. For marketplace lending to become a viable and sustainable alternative to bank lending platforms, they must better evaluate, monitor, and manage tail risk in marketplace loans and develop tools to monitor and manage financial risk losses.

The purpose of this paper is to perform Shariah review of Brownian motion that is used for prediction of Islamic stock prices and their volatility.

It uses the Shariah compliant development model guidelines to review the Brownian motion and its applications.

The model of Brownian motion does not involve any variable that renders it non-Shariah compliant; neither all applications of Brownian motion are Shariah compliant. Because the model is based on stochastic properties that involve randomness, therefore the issue of gharar takes the utmost important to handle in the applications of the model. The results need to be analyzed strictly in accordance with the Shariah whether they create any element of gharar or uncertainty in case of expected price and volatility estimates.

The research suffers from the limitation that it analyses only one model of physics, i.e. Brownian motion model from Shariah perspective.

The research opens an area for Shariah analysis of results generated from the application of advanced models of physics on matters related to Islamic financial markets.

The originality of this study stems from the fact that to the best of the authors’ knowledge, it is the first study that extends Shariah guidelines into Financial physics for making the foundations of Islamic econophysics.

This chapter explores other theoretical explanations to the commonly observed phenomenon of negatively skewed performance outcomes and inverse risk-return relationships in empirical firm data. The analysis conducted in many prior studies have implicated direct causal dependencies between performance and risk, or vice versa, with the possibility of simultaneous two-way relationships that are harder to discern. It is also shown how spurious artifacts deriving from the arithmetic links between mean and variance associate left-skewed distributions with negative mean variance correlations. However, the heterogeneous display of response capabilities among firms that compete in the same industry contexts may provide an alternative explanation for the observed performance characteristics. This is expressed as strategic responsiveness where performance outcomes with high negative skewness and excess kurtosis derive from heterogeneous adaptive processes among firms as they respond to a dynamic environment with different degrees of success. We test these results in different simulated competitive contexts disrupted by major unexpected events and find robust results across different environmental scenarios. The analysis looks at two different response processes, one modeled as conventional adaptive planning following an annual budget cycle, and another modeled as interactive updating where executives have frequent informative budget discussions with operating managers in the firm. The computational simulations show that interactive updating generates outcomes with higher returns and lower performance risk for moderate learning levels and restructuring costs. However, the resulting performance distributions are not as left-skewed as those observed in the empirical data that show higher resemblance to the adaptive planning outcomes.

The purpose of this study is to analyse and compile the literature on various option pricing models (OPM) or methodologies. The report highlights the gaps in the existing literature review and builds recommendations for potential scholars interested in the subject area.

In this study, the researchers used a systematic literature review procedure to collect data from Scopus. Bibliometric and structured network analyses were used to examine the bibliometric properties of 864 research documents.

As per the findings of the study, publication in the field has been increasing at a rate of 6% on average. This study also includes a list of the most influential and productive researchers, frequently used keywords and primary publications in this subject area. In particular, Thematic map and Sankey’s diagram for conceptual structure and for intellectual structure co-citation analysis and bibliographic coupling were used.

Based on the conclusion presented in this paper, there are several potential implications for research, practice and society.

This study provides useful insights for future research in the area of OPM in financial derivatives. Researchers can focus on impactful authors, significant work and productive countries and identify potential collaborators. The study also highlights the commonly used OPMs and emerging themes like machine learning and deep neural network models, which can inform practitioners about new developments in the field and guide the development of new models to address existing limitations.

The accurate pricing of financial derivatives has significant implications for society, as it can impact the stability of financial markets and the wider economy. The findings of this study, which identify the most commonly used OPMs and emerging themes, can help improve the accuracy of pricing and risk management in the financial derivatives sector, which can ultimately benefit society as a whole.

It is possibly the initial effort to consolidate the literature on calibration on option price by evaluating and analysing alternative OPM applied by researchers to guide future research in the right direction.

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.

With the evolution of the turbulent environment constantly triggering the emergence of a trust crisis between organizations, how can university–industry (U–I) alliances respond to the trust crisis when conducting green technology innovation (GTI) activities? This paper aims to address this issue.

The authors examined the process of trust crisis damage, including trust first suffering instantaneous impair as well as subsequently indirectly affecting GTI level, and ultimately hurting the profitability of green innovations. In this paper, a piecewise deterministic dynamic model is deployed to portray the trust and the GTI levels in GTI activities of U–I alliances.

The authors analyze the equilibrium results under decentralized and centralized decision-making modes to obtain the following conclusions: Trust levels are affected by a combination of hazard and damage (short and long term) rates, shifting from steady growth to decline in the presence of low hazard and damage rates. However, the GTI level has been growing steadily. It is essential to consider factors such as the hazard rate, the damage rate in the short and long terms, and the change in marginal profit in determining whether to pursue an efficiency- or recovery-friendly strategy in the face of a trust crisis. The authors found that two approaches can mitigate trust crisis losses: implementing a centralized decision-making mode (i.e. shared governance) and reducing pre-crisis trust-building investments. This study offers several insights for businesses and academics to respond to a trust crisis.

The present research can be extended in several directions. Instead of distinguishing attribution of trust crisis, the authors use hazard rate, short- and long-term damage rates and change in marginal profitability to distinguish the scale of trust crises. Future scholars can further add an attribution approach to enrich the classification of trust crises. Moreover, the authors only consider trust crises because of unexpected events in a turbulent environment; in fact, a trust crisis may also be a plateauing process, yet the authors do not study this situation.

First, the authors explore what factors affect the level of trust and the level of GTI when a trust crisis occurs. Second, the authors provide guidelines on how businesses and academics can coordinate their trust-building and GTI efforts when faced with a trust crisis in a turbulent environment.

First, the interaction between psychology and innovation management is explored in this paper. Although empirical studies have shown that trust in U–I alliances is related to innovation performance, and scholars have developed differential game models to portray the GTI process, building a differential game model to explore such an interaction is still scarce. Second, the authors incorporate inter-organizational trust level into the GTI level in university–industry collaboration, applying differential equations to portray the trust building and GTI processes, respectively, to reveal the importance of trust in CTI activities. Third, the authors establish a piecewise deterministic dynamic game model wherein the impact of crisis shocks is not equal to zero, which is inconsistent with most previous studies of Brownian motion.

Cross-layer approach in media access control (MAC) layer will address interference and jamming problems. Hybrid distributed MAC can be used for simultaneous voice, data transmissions in wireless sensor network (WSN) and Internet of Things (IoT) applications. Choosing the correct objective function in Nash equilibrium for game theory will address fairness index and resource allocation to the nodes. Game theory optimization for distributed may increase the network performance. The purpose of this study is to survey the various operations that can be carried out using distributive and adaptive MAC protocol. Hill climbing distributed MAC does not need a central coordination system and location-based transmission with neighbor awareness reduces transmission power.

Distributed MAC in wireless networks is used to address the challenges like network lifetime, reduced energy consumption and for improving delay performance. In this paper, a survey is made on various cooperative communications in MAC protocols, optimization techniques used to improve MAC performance in various applications and mathematical approaches involved in game theory optimization for MAC protocol.

Spatial reuse of channel improved by 3%–29%, and multichannel improves throughput by 8% using distributed MAC protocol. Nash equilibrium is found to perform well, which focuses on energy utility in the network by individual players. Fuzzy logic improves channel selection by 17% and secondary users’ involvement by 8%. Cross-layer approach in MAC layer will address interference and jamming problems. Hybrid distributed MAC can be used for simultaneous voice, data transmissions in WSN and IoT applications. Cross-layer and cooperative communication give energy savings of 27% and reduces hop distance by 4.7%. Choosing the correct objective function in Nash equilibrium for game theory will address fairness index and resource allocation to the nodes.

Other optimization techniques can be applied for WSN to analyze the performance.

Game theory optimization for distributed may increase the network performance. Optimal cuckoo search improves throughput by 90% and reduces delay by 91%. Stochastic approaches detect 80% attacks even in 90% malicious nodes.

Channel allocations in centralized or static manner must be based on traffic demands whether dynamic traffic or fluctuated traffic. Usage of multimedia devices also increased which in turn increased the demand for high throughput. Cochannel interference keep on changing or mitigations occur which can be handled by proper resource allocations. Network survival is by efficient usage of valid patis in the network by avoiding transmission failures and time slots’ effective usage.

Literature survey is carried out to find the methods which give better performance.