Higher strong order methods for linear Itô SDEs on matrix Lie groups

In this paper we present a general procedure for designing higher strong order methods for linear Itô stochastic differential equations on matrix Lie groups and illustrate this strategy with two novel schemes that have a strong convergence order of 1.5. Based on the Runge–Kutta–Munthe–Kaas (RKMK) method for ordinary differential equations on Lie groups, we present a stochastic version of this scheme and derive a condition such that the stochastic RKMK has the same strong convergence order as the underlying stochastic Runge–Kutta method. Further, we show how our higher order schemes can be applied in a mechanical engineering as well as in a financial mathematics setting.

An Italian perspective on the development of financial mathematics from 1992 to 2008

This paper is intended to be a survey of the development of financial mathematics as seen through the events that I organised, and partly co-organised, between 1992 and 2008. These events all took place in Italy between 1992 and 2003, while in 2008 I was involved in the organisation of an entire special semester in Linz (Austria); this semester is included here because it marks quite well the state-of-the-art of the period just before the so-called big financial crisis that lasted from, roughly, 2008 to 2012. Even if the survey may be affected by my personal views, it can still be seen as reflecting the actual global development since what I am going to describe here concerns major occurrences. For completeness, I also mention, although only briefly, some events that took place in Italy during the given period, but where I was not personally involved.

Analysis of Facebook in the Teaching-Learning Process about Mathematics Through Data Science

The aim of this quantitative research is to analyze the impact of Facebook in the teaching-learning process in financial mathematics education, using data science, machine learning, and neural networks. The sample is composed of 46 students from the Bachelor of Administration, Commerce and Marketing program at La Salle University. The results of machine learning (linear regression) indicate that sending messages, watching instructional videos, and publishing exercises on Facebook supports the teaching-learning process in financial mathematics. Likewise, data science identified six predictive models for the use of Facebook in the educational context, by means of the decision tree technique. Analysis using neural networks identified the influence of sending messages, watching instructional videos, and publishing exercises on Facebook during the assimilation of knowledge and development of mathematical skills. Finally, Facebook is a technological and communication tool that transforms the organization of teaching and learning activities in financial mathematics education.

Preface

International Conference on Mathematical and Statistical Sciences (ICMSS) 2021 Study Program of Mathematics and the Study Program of Statistics Faculty of Mathematics and Natural Sciences Universitas Lambung Mangkurat Banjarbaru - Indonesia, 15 - 16 September 2021 The International Conference on Mathematical and Statistical Sciences (ICMSS) 2021 was organized through a collaboration between the Study Program of Mathematics and the Study Program of Statistics, Faculty of Mathematics and Natural Sciences - Universitas Lambung Mangkurat (ULM). The theme raised was “Mathematical and Statistical Sciences in Multidisciplinary Research”, with the aims are to acknowledge, learn, share, and transfer the results of scientific knowledge and research among academia and practitioners who have used or implemented Mathematical and Statistical Sciences to solve real-world problems and improve the quality of life. The scopes of our conference are Mathematical modeling, Artificial intelligence, Mathematical physics, Algebra and its applications, Statistics and its applications, Computational fluid dynamics, Data mining and its applications, Dynamical nonlinear systems, Mathematics Educations, Financial mathematics, Mathematical biology, Numerical methods and analysis, Operation research and optimizations, and Real analysis. On behalf of the committee, we would like to thank the Rector of Universitas Lambung Mangkurat, the Dean of Faculty of Mathematics and Natural Sciences, Coordinator of the Study Program of Mathematics and Coordinator of the Study Program of Statistics, advisory board, steering committee, all committee members, reviewers, presenters, and participants. We also would thank the Indonesian Mathematical Society (IndoMS), The Indonesian Algebra Society (IAS), and The Forum Pendidikan Tinggi Statistika (Forstat). Special thanks are also given to the Journal of Physics: Conference Series. We, on behalf of the ICMSS 2021 committee, would like to thank all parties for their participation in supporting this publication. We hope to see you all at the next conference. Kind regards, Dr. Muhammad Ahsar Karim Chair of the ICMSS 2021 List of Organizing Committees, Photographs and Peer review statement are available in this pdf.

“Generación de Preguntas Aleatorias Calculadas, para evaluar el tema de Monto dentro del capítulo de Interés Simple en un curso de Matemática Financiera”

El presente trabajo de investigación fue realizado en el año 2020 y 2021, durante la pandemia del COVID-19, es importante hacer esta puntualización puesto que la educación universitaria por años obvió la enseñanza virtual, utilizando las plataformas web como un método optativo al principio, sin embargo, dentro del contexto actual pasaron a ser obligatorias. En este punto del resumen se tiene que aclarar que la herramienta de gestión de aprendizaje, o LMS con el que se trabajo es el Moodle. Es por ello, que fue lanzada a mediados del año 2020 al entorno virtual para los procesos educativos permitiendo una mejor comunicación relativamente entre participantes, también para el desarrollo colectivo e individual del aprendizaje, y siendo parte de ello, la evaluación. La evaluación de los estudiantes es una etapa crítica del proceso educativo, puesto que si es de bajo nivel los estudiantes serán aprobados sin que hayan asimilado los conocimientos mínimos, por el contrario, si es muy estricta probablemente un porcentaje elevado de estudiantes no aprobarían la materia. Por otra parte, el hecho de que los alumnos manejen muy bien las herramientas tecnológicas de esta época provoca que los docentes se sientan presionados durante el proceso de evaluación, puesto que la posibilidad de que los estudiantes se vean tentados a ver las pruebas individuales como evaluaciones colaborativas (grupales) aumenta considerablemente. ¿Cómo han tratado los docentes de inmunizar (usando terminología de estos días) nuestras evaluaciones contra esta posibilidad?, el arsenal de opciones con el que viene equipado el LMS Moodle es variado, se requiere valorar la potencia del tipo de pregunta calculada a la luz del tema que se quiere evaluar, sobre el nivel educativo (que es el universitario), el ciclo en el que se encuentran nuestros estudiantes (al principio de sus carreras, en la mitad o finalizando), los pre-requisitos que tiene la asignatura y finalmente la capacidad que se tenga para poder implementar las preguntas. Lo que se pretende hacer en este artículo es compartir como se han implementado preguntas calculadas, generadas aleatoriamente para evaluar el tema específico del cálculo de monto, dentro del capítulo de Interés Simple de un curso de Matemáticas Financieras utilizando preguntas calculadas que son generadas a partir de un conjunto de datos que se pueden especificar. To contextualize, this article was written in 2021 during the COVID-19 pandemic, it is important to make this point since university education for years obviated virtual teaching, using web platforms as an optional method at the beginning, however, within the current context they became mandatory. At this point in the summary, we have to clarify that the learning management tool, or LMS with which we work is Moodle. That is why it was launched in mid-2020 to the virtual environment for educational processes, allowing relatively better communication between participants, also for the collective and individual development of learning, and being part of it, evaluation. The evaluation of students is a critical stage of the educational process, since if it is of a low level, students will be approved without having assimilated the minimum knowledge, on the contrary, if it is very strict, a high percentage of students would probably not pass the subject. On the other hand, the fact that students handle the technological tools of this time very well causes teachers to feel pressured during the evaluation process, since the possibility that students are tempted to see individual tests as evaluations collaborative (group) increases considerably. How have we teachers tried to immunize (using terminology of these days) our evaluations against this possibility? The arsenal of options with which the LMS Moodle is equipped is varied, we need to assess the power of the type of question calculated in light of the subject that we want to evaluate, on the educational level (which is university), the cycle in which our students are (at the beginning of their careers, in the middle or at the end), the prerequisites that the subject has and finally the capacity that we have to be able to implement the questions. What we intend to do in this article is to share how we have implemented calculated questions, randomly generated to evaluate the specific topic of calculating the amount, within the Simple Interest chapter of a Financial Mathematics course using calculated questions that are generated from a set of data that we can specify.

Special Issue “Interplay between Financial and Actuarial Mathematics”

The Special Issue aims to highlight the interaction between actuarial and financial mathematics, which, due to the recent low interest rates and implications of COVID-19, requires an interlace between actuarial and financial methods, along with control theory, machine learning, mortality models, option pricing, hedging, unit-linked contracts and drawdown analysis, among others [...]