Is What a Physician Does Really That Different from What an Actuarial Mathematician Does?
By José Daniel López-Barrientos
Innovators & Entrepreneurs, February 2024
In essence, yes. But from a certain point of view, no. Our family’s doctor once told us that his professional practice rests upon four pillars: His consultation with patients, researching new and exciting topics for him, teaching the younger generations, and management tasks (such as keeping the payroll of his office in control, maintaining his connections with his colleagues around the world and taking care of the rent of his facilities). For a professional researcher, things are not that different. Indeed, the only things that change are the prioritization of each of those pillars and, of course, the domain of exercise.
In my case, as a researcher for the Faculty of Actuarial Sciences at the Universidad Anáhuac México, the order of these activities is as follows. First comes my own scientific research. Next are my teaching obligations with my undergraduate and graduate students. The third priority is my managerial and operational tasks. The fourth priority is the consultation activities I develop for the enterprises with a signed agreement with the University. It is worth mentioning that these companies are attracted to the team I represent because of the innovations that stem from our research.
Naturally, depending on the workload of a particular day, or the season of the year, the activities in the list of priorities may climb up or fall down in the hierarchy. For example, although the preparation of the courses for the next term during the holiday seasons remains as one of the main activities of the agenda, in these periods, my consulting assignments take precedence, and these tasks switch their places. Another example of trading places is when I need to prepare a report for the University itself, or for a third party in account of, for instance, the University application to upgrade its current level in the Society of Actuaries’ classification of “Universities and Colleges with an Actuarial Program.” In these cases, reporting and managing applications become the first priority, and my research is relegated to the fourth place in my list of priorities. However, the main source of work of all four pillars is my research labor.
My research is mainly devoted to applications of stochastic control for one and multiple agents in areas related to the measurement, prevention, and mitigation of risk. For instance, my research team published a series of research papers on the time-until-exhaustion/breakdown of extraction wells of non-renewable resources, which eventually led my group to write a couple of papers on the actuarial reserve to insure extraction tasks. See López Barrientos, 2022;[1] Real-Miranda and López-Barrientos, 2022a,[2] and 2022b;[3] and the references therein. The first of these papers was granted an award on behalf of the Asociación Mexicana de Actuarios (AMA) in 2021, while the other two are the backbones of the Doctoral dissertation of Rigoberto Real-Miranda, Ph.D.
The AMA granted yet another award to one of my Doctoral students and myself for a paper on a new methodology to compute the probability of ruin of a pension fund for a population by means of a central limit theorem in the context of the optimization of a variation of the classic Cramér-Lundberg ruin model that takes into account a stochastic process for premia (see Lopez Barrientos and Plata Gallegos, 2024).[4] In that research, the controller is the proportion of the salary invested by each member of the working force to the end of contributing to their own pension fund and to the pensions of the senior citizens. One of our assumptions is the the actuarial equivalence between the costs of financing of the defined contribution and the defined benefit schemas we studied earlier in Aguirre Farías et al., 2019.[5]
A critical tool we used to write the latter award-winning article was the series of mathematical results contained in López-Barrientos et al., 2024.[6] This paper studies a mean-field approach for Markov decision processes (MDP) in a class of systems of a large number of objects that interact with each other according to an observable (but unknown) probability law for the central controller. The central controller acts under the so-called ergodic cost criterion with Borel state and control spaces, bounded costs, and compact action space in an MDP. We depart from the characterization of the discounted optimal strategies, and then, by means of an Abelian theorem, we study the existence of average cost optimal stationary policies in the original model.
My research group is currently working on a plausible extension of the results just mentioned above. Instead of considering degenerate games (games with only one player), we are developing the corresponding theory to mathematically characterize the situation where several agents try to profit from a system where a large number of objects interact with each other according to an observable (but unknown) probability law. The main applications we have found so far include a model to ease the pernicious effect of crime on the avocado industry of Michoacán, the Mexican state responsible for the largest production and exportation of avocado in the world; and also a proposal for the participants in the Mexican industry of insurance to release their full potential in terms of the market share they control through time on an infinite horizon. The first application has taken us to study n-player Voronoi games on a bounded set in the plane in the presence of an initial set of allocations. Our second interest has given us a chance to delve into the use of neural networks to characterize the behavior of the costumers of insurance companies in a given market. My research group has three separate drafts, each dealing with one of the aspects recently addressed.
As (hopefully) can be seen from the above paragraphs, my research activities feed my teaching, my consultation tasks, and my managerial and operational actions. In spite of the facts that I speak/write from a very personal (and therefore particular) point of view, and that I lack formal proof of the following statement: The bottom line is that the professional development of all practitioners in any field of domain has (at least) the same four topic areas, and they are prioritized according to the responsibilities of the subject under consideration. What is your case? Do you agree that it all boils down to operating, teaching, consulting, and researching (O-T-C-R) and its anagrams? My family’s doctor would!
Statements of fact and opinions expressed herein are those of the individual authors and are not necessarily those of the Society of Actuaries, the newsletter editors, or the respective authors’ employers.
José Daniel López-Barrientos obtained his bachelor's degree in actuarial sciences in 2003 from Universidad Anáhuac México. He graduated from the Masters’ and Doctoral programs in Mathematics at the Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional (Center of Research and Advanced Studies of the National Polytechnic Institute) in México City in 2006 and 2012, respectively. He occupied postdoctoral positions at the Haute École de Commerce in Montreal in 2015; and at the Санкт-Петербургский Государственный Университет (State University of Saint Petersburg) in 2018. He is a member of the Mexican National System of Researcher since 2012 and has advised three Doctoral students so far. He has had the opportunity to teach in many universities from his own country, and in Guatemala, Peru, Russia and Senegal (the latter of these experiences is due to his involvement in the Actuarial Educators Network of the International Actuarial Association). Currently, he is an active member of the Mexican Colegio Nacional de Actuarios and he carries on his professional activities at the Faculty of Actuarial Sciences in his Alma Mater, Universidad Anáhuac México.
Endnotes
[1] José Daniel López-Barrientos (2022) “Cómo evitar que la industria petrolera se quede sin seguros” in Revista Mexicana de Investigación actuarial aplicada Actuarios Trabajando, 12: 152-164.
[2] Rigoberto Real-Miranda and José Daniel López-Barrientos (2022a). “A geologic-actuarial approach for insuring the extraction tasks of non-renewable resources by one and two agents.” Mathematics, 10(13), 2242.
[3] Rigoberto Real-Miranda and José Daniel López-Barrientos (2022b). “Reserva matemática actuarial para la extracción de recursos no-renovables a partir de variables de pérdida no-negativas.” Revista Electrónica de Comunicaciones y Trabajos de la Asociación de Profesores Universitarios de Matemáticas aplicadas a la Economía y la Empresa, 23(2): 95-117.
[4] José Daniel López-Barrientos and Humberto Plata Gallegos (2024). “Una nueva aproximación a la constitución de una reserva actuarial de arriba p’abajo.” To appear in Revista Mexicana de Investigación actuarial aplicada Actuarios Trabajando, 15.
[5] Francisco Miguel Aguirre Farías, Francisco Miguel Aguirre Villarreal, and José Daniel López-Barrientos (2019). “Comparison of the costs of the defined-benefit and the defined-contribution schemes under an actuarial methodology” in Revista Mexicana de Economía y Finanzas Nueva Época, 14(4): 671-691.
[6] José Daniel López-Barrientos, José Manuel Mendoza-Madrid and Paola Friné González-Vega (2024). “An Abelian theorem for a mean-field MDP with unknown law.” To appear in Pure and Applied Functional Analysis, 9(4).