A fourth-order collocation scheme for generalized Black-Scholes model in financial decision-making

ABSTRACTWomen’s economic empowerment remains an important global policy issue and their involvement in household decision-making is critical for development. This paper aims to elucidate a key feature of bargaining models of intra-household decision-making, namely the dynamics between women’s economic bargaining power and their financial decision-making power. The paper also documents trends and transitions in financial decision-making. Using balanced panel data from South Africa’s National Income Dynamics Study (NIDS), the analysis finds that women who are married or living together remain economically disadvantaged compared to their male counterparts. Although gaining ground in terms of financial decision-making responsibility, women also remain disadvantaged compared to men in terms of financial decision-making power. Yet, employment opportunities significantly enhances women’s role in financial decision-making, thus arguing a case for continued efforts at women’s economic empowerment.

Adopting behavioural finance as a theory has emerged as an important field due to its opposition to finance principles that rely on rational decision-making and efficient market models. The research investigates behavioural finance elements that affect risk perception (RP) processes and financial decision-making (FDM) in equity market activities. Traditional finance depends on efficient markets with rational behaviour, but behavioural finance focuses on analyzing how psychological biases affect market participants. The Research Investigated the factors such as herding, disposition effect (DE), overconfidence, loss aversion (LA), and mental accounting (MA) that influence FDM with RP acting as a mediator. A total of 300 individual investors participated in the online survey, but researchers validated data from the responses of 270 participants. IBM SPSS version 26 employed SEM to evaluate the data collected. A Multiple Regression Analysis (MRA) evaluated how the behavioural finance factors impact FDM decision-making, while a Confirmatory Factor Analysis (CFA) tested the measurement model reliability. Research data shows that RP experiences meaningful changes due to herding behaviour and disposition effect, LA, and mental accounting, but overconfidence, along with over-optimism, directly affects FDM without changing RP levels. The link between RP and financial decisions is positive, and every behavioural variable affects investment choices indirectly through RP assessment. This demonstrates that behavioural biases affect investment choices, so investigators recommend that psychological factors become integral to the risk management framework creation. Investigator teams examine supplementary behavioural elements that enhance exposure to danger assessment while studying population and ethnic influences on investment actions.

Focal Versus Background Goals in the Choice of Investment Products: Trading Off Financial Returns for Self-Expression?

Entropic approximate learning for financial decision-making in the small data regime

This study presents a graph neural network (GNN)-based framework for corporate default risk prediction by explicitly modeling inter-firm dependencies through supply-chain links, ownership ties, and board overlaps. We construct a heterogeneous information network (HIN) from longitudinal firm-level data (20142024), transforming relational structures into learned node embeddings via a three-layer relational graph convolutional network (R-GCN). These embeddings are further processed by a survival-analysis layer to estimate time-varying default probabilities. Compared to traditional financial ratio models and graph-agnostic machine learning baselines, the proposed GNN consistently outperforms in terms of AUC, F1-score, and Harrells C-index. Extensive ablation studies confirm the importance of incorporating economic relationships, particularly supply-chain dependencies, which exhibit the highest marginal contribution to predictive performance. Moreover, the model demonstrates robustness across economic cycles, including during the COVID-induced stress period. A case study further illustrates how GNN-based message passing reveals upstream contagion paths not captured by standalone financial metrics. The findings highlight the significant value of network-aware credit risk modeling in regulatory supervision and financial decision-making. Our approach suggests that integrating network topology into corporate risk assessment can offer timely, interpretable, and materially superior insights for early warning systems and financial resilience analysis.

We consider the problem of pricing American options using the generalized Black–Scholes model. The generalized Black–Scholes model is a modified form of the standard Black–Scholes model with the effect of interest and consumption rates. In general, because the American option problem does not have an exact closed-form solution, some type of approximation is required. A simple numerical method for pricing American put options under the generalized Black–Scholes model is presented. The proposed method corresponds to a free boundary (also called an optimal exercise boundary) problem for a partial differential equation. We use a transformed function that has Lipschitz character near the optimal exercise boundary to determine the optimal exercise boundary. Numerical results indicating the performance of the proposed method are examined. Several numerical results are also presented that illustrate a comparison between our proposed method and others.

Artificial intelligence (AI) is reshaping financial decision-making processes by enhancing analytical precision, reducing uncertainty, and enabling data-driven strategies. This research proposes an AI-driven strategic decision-support framework to optimize financial decision models in complex, uncertain environments. The framework integrates predictive analytics and optimization algorithms to help financial managers and policymakers improve investment decisions, risk assessment, and resource allocation. Building on decision-engineering principles, the study conceptualizes a hybrid model combining elements of machine learning, data analytics, and cognitive decision theory to strengthen the robustness and adaptability of strategic financial decisions. The proposed approach is structured to accommodate dynamic financial and market data, allowing for continuous improvement of forecasts and decision outcomes as new information becomes available. Preliminary results suggest that AI-enhanced decision frameworks can improve forecasting reliability and strategic responsiveness, particularly in contexts characterized by volatility and incomplete information. This research contributes to the growing body of work at the intersection of artificial intelligence and financial management, offering both theoretical and practical insights for the design of intelligent financial systems. This conceptual study also lays the groundwork for a forthcoming empirical validation using financial datasets to evaluate the framework’s robustness and adaptability.

Employee Stock Option Plans (ESOPs) have gained prominence as a successful HR strategy that improves the employees’ performance and enables the company to have an economic and strategic advantage. However, the time at which employees decide to exercise their options determines the incentive that they derive from the stock options granted to them. It is one of the crucial financial decisions which can have immense implications for both employers and employees. According to the Black Scholes Model, an option's value is maximum when it is held until maturity. But most employees exercise their options early, which comes with a cost to both the employee and the company. It can be attributed to the fact that when faced with financial decisions the individuals do not always refer to complex finance models and formulas and make decisions rationally. Instead they resort to mental accounting and shortcuts leading to bounded rationality that can unconsciously impact their decision-making process. This paper explores the literature available on behavioral factors and biases that in addition to rational factors can affect the exercise of employee stock options.

The increasing complexity of financial systems and strategic environments has intensified the need for advanced decision-making models capable of handling uncertainty, multidimensional risk, and dynamic optimization constraints. Classical management science tools—while robust—often face computational limitations when applied to high-dimensional portfolio optimization, capital allocation, and scenario-based strategic planning. This paper explores quantum-driven financial decision-making models for management science and strategic planning, emphasizing hybrid quantum–classical frameworks that integrate quantum optimization, probabilistic sampling, and advanced analytics into managerial decision systems. By examining applications in portfolio management, risk assessment, supply chain finance, and strategic resource allocation, the study evaluates the theoretical advantages and practical constraints of quantum-enhanced models in organizational contexts. The findings suggest that quantum-driven decision architectures may complement traditional financial models by expanding solution-space exploration and improving optimization efficiency, thereby enhancing strategic agility and long-term value creation.

The paper offers a comparison of household financial decision-making models considering a household as one of the initial economic units, understanding the decision-making process and utility function perception of which is influential for the conception of the integrate economic development of a society. Paper provides a brief description of the most applicable within- household decision-making models, namely unitary, bargaining, and collective ones, denoting the pros and cons of their employment for experimental investigation by stating the appropriateness conditions, which are as follows: the ability to include more than two members considering their own preferences, various possible scope of modelled decisions, and framework allowing for empirical research. Regarding previous research, the collective model with Pareto weights appears to be the one, which justifies the conditions set.

Rapid development of financial markets resulted new challenges for both investors and investment issues. This increased demand for innovative, modern investment and portfolio management decisions adequate for market conditions. Financial market receives special attention, creating new models, includes financial risk management and investment decision support systems.Researchers recognize the need to deal with financial problems using models consistent with the reality and based on sophisticated quantitative analysis technique. Thus, role mathematical modeling in finance becomes important. This article deals with various investments decision-making models, which include forecasting, optimization, stochatic processes, artificial intelligence, etc., and become useful tools for investment decisions.

The study examines the development and formation of behavioral corporate finance based on various theories and the work of scholars, highlighting the key stages and their distinctive features. A comparative analysis of different behavioral economic approaches has been conducted. The paper analyzes the current state of national and foreign achievements, as well as the conceptual foundations for the development of behavioral corporate finance. Currently, behavioral sciences have become one of the key tools for predicting economic behavior at the micro, meso, and macro levels. Behavioral corporate finance has emerged as a distinct field at the intersection of finance, economics, neuroscience, and psychology. It explains corporate managers’ decision-making processes and forecasts irrational behavior influenced by emotions and cognitive biases, which affect corporate strategy and capital structure. The relevance of the study increases, particularly during critical economic periods when the level of irrational corporate behavior rises and the level of objective analysis decreases due to uncertainty. An analysis of corporate governance and financial decision-making shows that managerial behavior often deviates from the traditional rational decision-making model due to emotional and cognitive factors. Loss aversion, overconfidence, the status quo effect, and irrational optimism are the key factors influencing financial decisions. The key factors for studying behavioral corporate finance in Ukraine include: 1. The impact of globalization processes and the complexity of corporate processes. 2. Deviations from the rational model in corporate decision-making. 3. The lack of clear forecasting in investment and dividend policies due to the influence of social and psychological biases. 4. The low level of implementation of behavioral approaches in Ukraine. Behavioral corporate finance is actively applied in developed countries, especially in the United States, the United Kingdom, and Western European countries. This enhances the profitability of mergers and acquisitions, encourages the closure of low-profit business segments, and increases the use of internal financing (e.g., share buybacks by Apple and Microsoft). It also reduces debt financing (e.g., Tesla), ensures stability in dividend policies (e.g., Johnson & Johnson, Coca-Cola), promotes investment conservatism (e.g., Berkshire Hathaway), and reduces the risk of underestimating the management of target companies during acquisitions. In conclusion, the development and implementation of behavioral corporate finance at the national level are essential for further improving corporate governance and enhancing the quality of corporate financial strategies during periods of economic instability.

The Covid-19 Pandemic has shifted the behaviour of decision-makers in all business processes. This situation has accelerated the process of digitizing all information, information technology, and business processes. As a subsidiary of an Oil and Gas State-Owned Enterprise in Indonesia, The SHU also has a similar SOE's bureaucracy for the approval process in business development. What factors were considered, and how did the interaction and interrelation within those factors influence the decision-making is the main question in this research. This research aims at developing the decision-making system by accommodating the decision-maker's needs and preferences. Action research based on soft systems methodology (SSM) is used to model the new decision-making system and compare results. The long decision-making stages of business development investment have delayed several important business development projects, leading to missed early production opportunities and increased capital investment. Financial decision documents have to be wet-signed by all stakeholders involved in the decision -making process. It is practically difficult to follow existing business processes for business development approval during the Pandemic. The Covid-19 Pandemic is an entry point for redefining existing decision-making systems. The results showed that the principle of prudence and compliance are the main factors influencing decision-making. The development of digital review and approval based on a decision-making system conceptual model accommodated the interests of all stakeholders, and business processes continued during the Pandemic

We establish existence of Predictable Forward Performance Processes (PFPPs) in conditionally complete markets, which has been previously shown only in the binomial setting. Our market model can be a discrete-time or a continuous-time model, and the investment horizon can be finite or infinite. We show that the main step in construction of PFPPs is solving a one-period problem involving an integral equation, which is the counterpart of the functional equation found in the binomial case. Although this integral equation has been partially studied in the existing literature, we provide a new solution method using the Fourier transform for tempered distributions. We also provide closed-form solutions for PFPPs with inverse marginal functions that are completely monotonic and establish uniqueness of PFPPs within this class. We apply our results to two special cases. The first one is the binomial market and is included to relate our work to the existing literature. The second example considers a generalized Black–Scholes model which, to the best of our knowledge, is a new result.

In this article we compare the profit and loss arising from the delta-neutral dynamic hedging of options, using two possible values for the delta of the option. The first is the Black–Scholes implied delta, while the second is the local delta, namely the delta of the option in a generalized Black–Scholes model with a local volatility, recalibrated to the market smile every day. We explain why, in negatively skewed markets, the local delta should provide a better hedge than the implied delta during slow rallies or fast sell-offs, and a worse hedge, although to a smaller extent, during fast rallies or slow sell-offs. Since slow rallies and fast sell-offs are more likely to occur than fast rallies or slow sell-offs in negatively skewed markets (provided we have physical as well as implied negative skewness), we conclude that, on average, the local delta provides a better hedge than the implied delta in negatively skewed markets. We obtain the same conclusion in the case of positively skewed markets. We illustrate these results using both simulated and real time-series of equity-index data, which have had a large negative implied skew since the stock market crash of October 1987. Moreover, we check numerically that the conclusions we draw are true when transaction costs are taken into account. In the last section we discuss the case of barrier options.