Stochastic Models in Population Dynamics and Finance

Grant PID2024-158823NB-I00 funded by

Description: Motivated by its applications to population dynamics and finance, the project aims to contribute to the general theory of stochastic processes (in particular, time-homogeneous and time-inhomogeneous Markov chains, and related processes) and the stochastic calculus of Itô and Malliavin by theoretically studying models that underlie three sufficiently differentiated application contexts.

Line 1: Markov models in the transmission of pathogens. The specific objectives of this line are: (1.a) the study of stochastic models for the transmission of pathogens in hospitals, which incorporate heterogeneity in the population due to the behaviour of individuals, the existence of mitigation strategies and environmental factors; (1.b) the study of stochastic models for the airborne transmission of pathogens in hospitals assuming population heterogeneity and the transient behaviour of individuals, by extending the Wells-Riley methodology; (1.c) the study of stochastic models for the transmission of pathogens in the presence of asymptomatic individuals, and the quantification of the effect of the presence of asymptomatic individuals on the overall incidence and persistence of the pathogen; and (1.d) the study of stochastic models for the transmission of pathogens in the presence of vaccination, isolation andquarantine measures, and the quantification of the effect of these control measures on the overall incidence and persistence of the pathogen.

Line 2: Stochastic models to formalize the strategic behavior of the customers. The specific objectives of this line are: (2.a) the analytical study of the impact of the information structure of a stochastic service system on the strategic behavior of its entities, as well as on the general (social) welfare and/or the administrator’s profit; (2.b) the analytical study of the strategic behavior of the customers in a stochastic service system under differentiated information structures; (2.c) the analytical study of the combined use of stochastic price/cost systems and mechanisms for providing information to users; and (2.d) the analytical study of stochastic systems with customer’s utility functions that incorporate risks associated with congestion.

Line 3: Stochastic models in financial mathematics. The specific objectives of this line are: (3.a) the development of stochastic tools, oriented towards the risk classification of financial entities, with the purpose of describing the risk of bankruptcy in the case of extreme weather events, and the study of new financial derivatives that are more resilient to climate change; (3.b) the design of automated exchange algorithms that preserve transparency and decentralization in crypto-financial systems, and optimization of investment portfolios based on the topology of the financial exchange network; (3.c) the study of the stochastic nature of volatility from the proposal of new stochastic models, of both mesoscopic and microscopic character, based on empirical data; and (3.d) the extension of stochastic tools, mainly based on Malliavin Calculus, arising in quantitative financial analysis to the solution of problems in termotechnics with potential applications in Engineering.

Keywords: Stochastic Processes; Stochastic Calculus; Queueing Models; Epidemic Models; Finance

Scheduling dates: 01/09/2025-31/08/2029

Members of the UCM-UNED research team:

Students at the UCM-UNED:

  • Jorge Bengoa Pinedo, Master’s student
  • María Alejandra di Césare, PhD student
  • Helder Rojas Molina, PhD student
  • Víctor David Sánchez González, PhD student

Collaborators outside the UCM-UNED:

Scientific papers:

Work in progress: 

  • Gómez-Corral A, López-Herrero MJ, Taipe D (2026) Time to admission and length of stay in an epidemic model with limited number of beds.
  • Marshall M, Elaldi N, Gould M, King MF, Molina-París C, Scarabel F, Lythe G, López-García M (2026) A stochastic model of nosocomial transmission: quantifying the impact of staff cohorting and patient isolation.
  • Gamboa M, López-Herrero MJ (2026) Hospital acquired infections in intensive care units operating under cyclic environmental conditions.
  • Gamboa M, López-Herrero MJ, Reyes-Nacimiento S (2026) Modeling pathogen transmission in emergency departments: the role of mitigation measures and crowding.
  • Gamboa M, Reyes-Nacimiento S (2026) The impact of asymptomatic individuals on pathogen spread in a stochastic SVAIS model with imperfect vaccination.

Communications in scientific conferences:

  • (Contributed talk) Erlangian approximations of epidemic models with time-varying contact and recovery rates, by A. Gómez-Corral. Workshop on Population Models in Biology, 2025. IMAG, University of Granada, Spain, November 2025.
  • (Contributed talk) On an epidemic model in a resource-limited environment, by A. Gómez-Corral, M.J. Lopez-Herrero and D. Taipe. 17th Conference on Dynamical Systems Applied to Biology and Natural Sciences (DSABNS 2026), mini-symposium «Quantitative Approaches to Infection Risk: Population, Enviroment, and Exposure». Granada, Spain, February 2026.
  • (Plenary talk) Optimal trading and routing in constant function market makers, by C. Escudero. International Conference on Optimization and Machine Learning: Theory and Applications (ICOMaLTA-2026). University of Tarapacá, Arica, Chile. May 2026.
  • (Contributed talk) Time until disease detection in a stochastic SVIR model with waning vaccine, by M.J. Lopez-Herrero. StochMod 2026. Centrum Wiskunde & Informatica (CWI) & Vrije Universiteit Amsterdam, Amsterdam, The Netherlands, June 2026.
  • (Plenary talk) Game-theoretic models in queueing theory, by A Economou. 5th International Workshop on Stochastic Processes and their Applications. University of Extremadura, Badajoz, Spain, June-July 2026.
  • (Contributed talk) Quantifying the impact of epidemics and the efficacy of imperfect vaccines in a stochastic SVIR model, by M. Gamboa. 5th International Workshop on Stochastic Processes and their Applications. University of Extremadura, Badajoz, Spain, June-July 2026.
  • (Contributed talk) A two-ward stochastic model for managing of hospital-acquired infections and patient isolation in switching environments, by M.J. López-Herrero and M. Gamboa. 5th International Workshop on Stochastic Processes and their Applications. University of Extremadura, Badajoz, Spain, June-July 2026.
  • (Contributed talk) Some measures for epidemic decision-making under limited resources in a stochastic SVIR model, by M. Gamboa, European Conference on Mathematical and Theoretical Biology 2026. University of Graz, Graz, Austria, July 2026.
  • (Contributed talk) Time until disease detection in a stochastic epidemic model with imperfect vaccination, by D. Taipe, European Conference on Mathematical and Theoretical Biology 2026. University of Graz, Graz, Austria, July 2026.

Other contributions:

  • (Webinar, keynote lecture) A qualitative financial risk classification in the presence of time oscillations and by means of first passage times, by C Escudero. Bukhtishu Publishing Group, December 2025.
  • (Seminar) Procesos QBD no-homogéneos en el tiempo analizados mediante Erlangización, by A. Gómez-Corral. Department of Statistics, Operations Research and Numerical Calculus, Universidad Nacional de Educación a Distancia, Spain, December 2025.
  • (Seminar) A three-level financial risk classification under time oscillations through first passage times, by C Escudero. Instituto de Computación Científica Avanzada de Extremadura, Universidad de  Extremadura, Spain, September 2025.

Popularization and dissemination of stochastic processes in population dynamics and related fields:

  • (Seminar) La música del azar: técnicas estocásticas y simulación en composición, by M Gamboa. Semana de la Ciencia y la Innovación de la Comunidad de Madrid, Facultad de Estudios Estadísticos, Universidad Complutense de Madrid, Spain, November 2025.
  • (Seminar) Bioestadística para corazones despiertos en ciencias de la salud, by J Borao, MJ López-Herrero & D Lora. Semana de la Ciencia y la Innovación de la Comunidad de Madrid, Facultad de Estudios Estadísticos, Universidad Complutense de Madrid, Spain, November 2025.
  • (Seminar) La aleatoriedad de las epidemias, by A Gómez-Corral. Ciclo de Conferencias IES García Morato, Madrid, Spain, December 2025.

Doctoral thesis:

  • Stochastic calculus beyond Itô: Hänggi-Klimontovich, equivalence and cloaking, by Helder Alan Rojas Molina. Universidad Nacional de Educación a Distancia. November 2025.

Related links:

Acknowledgements

This project is supported by grant PID2024-158823NB-I00 funded by MICIU/AEI/10.13039/501100011033/ and by ERDF, EU.