The rapid changes in information and communication technology (ICT), the increasing availability of processing power, and the complexity of mathematical software demand a radical re-thinking of science, technology, engineering, arts, and mathematics (STEAM), as well as mathematics education. In the transition to technology-based classrooms, the constant use of educational software is a requirement for sustainable STEAM and mathematics education. This software supports a collaborative and actionable learning environment, develops 21st-century skills, and promotes the adoption of active and innovative methodologies. This paper focuses on learning and teaching mathematics and analyzes the role and utility of ICT tools in education as computer algebra systems (CAS) and dynamic geometry systems (DGS) in implementing active and innovative teaching methodologies related to sustainable STEAM education. Likewise, it highlights the necessity for learners to have extensive knowledge of mathematical theory, an essential asset to ensure the reliable and effective use of mathematical software. Through a practical experiment, this study aims to highlight that a mixed teaching method can significantly improve the sustainability of math knowledge. It provides various solid examples of CAS and DGS applications to emphasize its usage rooted in a mathematical background to enable learners to identify when the computer solution is unreliable. The study highlights that the proper use of CAS and DGS is an efficient method of deepening our understanding of mathematical notions and solving tasks in STEAM subjects and real-life applications. This paper’s goal is to direct our attention to the proper and intelligent use of computer tools, especially symbolic calculators, such as CAS and DGS, without providing an in-depth analysis of the challenges of these technologies. The outcomes of the paper should offer educators and learners new elements of active strategies and innovative learning models that can be immediately applied in education.

The aim of the paper is to propose, and give an example of, a strategy for managing insurance risk in continuous time to protect a portfolio of non-life insurance contracts against unwelcome surplus fluctuations. The strategy combines the characteristics of the ruin probability and the values VaR and CVaR. It also proposes an approach for reducing the required initial reserves by means of capital injections when the surplus is tending towards negative values, which, if used, would protect a portfolio of insurance contracts against unwelcome fluctuations of that surplus. The proposed approach enables the insurer to analyse the surplus by developing a number of scenarios for the progress of the surplus for a given reinsurance protection over a particular time period. It allows one to observe the differences in the reduction of risk obtained with different types of reinsurance chains. In addition, one can compare the differences with the results obtained, using optimally chosen parameters for each type of proportional reinsurance making up the reinsurance chain.

Background: The significance of this study arises from the increasing complexity of managing insurance products, driven by the need to accurately model and predict the occurrence of insured events and associated risks. These processes are relevant not only to life insurance companies but to any institution offering personal insurance and supplementary coverages, such as banks, brokerage firms, and others. Existing literature highlights extensive possibilities for the application of stochastic processes in various fields, including finance, biology, and environmental engineering, with notable applicability in insurance. Purpose: This article aims to explore the application of stochastic models in the decision-making processes for managing insurance products. Specifically, it focuses on the development and utilization of multi-state models for pricing selected insurance products and analysing the impact of parameter changes on the amount of regular net premium. Study design/methodology/approach: We start with the traditional 'Healthy-Dead' model, which we extend to include the 'Sick' state. By restricting the transition from this state to the 'Healthy' state, we obtain a three-state 'Healthy-Sick-Dead' model for incurable critical illness. This is a non-homogeneous Markov process characterized by the respective transition probabilities. Actuarial calculations of transition probabilities are based on specific statistical data from an unnamed insurance company. The resulting regular net premium represents the real (net) price of the supplementary insurance product for incurable critical illness. Findings/conclusions: The main findings suggest that incorporating stochastic models into the creation and management of insurance products allows for more accurate predictions of insured events and better risk assessment. The introduced three-state model provides a robust framework for pricing supplementary insurance due to incurable critical illness. The analysis demonstrates how changes in transition probabilities affect the amount of net premium, underscoring the importance of precise parameter estimation. Limitations/future research: The study's limitations include reliance on accurate historical data, which may not fully capture future trends and changes in health outcomes, as experienced during the Covid-19 pandemic. Future research should explore the integration of a larger amount of real data and advanced computational methods for their processing. Additionally, extending the model to include the 'recovery' transition would enhance its applicability for 'all' types of critical illnesses. The creation of such an insurance product would, however, assume the availability of a large amount of high-quality data (Schmidt, 2021).