Hello and welcome!

Brief Bio

I am Joshué Helí Ricalde Guerrero (he/him). I am currently a postdoctoral researcher under the mentorship of Prof. Dylan Possamaï at the Department of Mathematics at ETH Zürich.

I obtained my PhD and my Master in Probability and Statistics from Centro de Investigación en Matemáticas (México) under the supervision of Prof. Daniel Hernández Hernández. Before that I obtained my BSc in Mathematical Engineering from Instituto Politécnico Nacional (México), and worked in the industry as a risk underwriter in one of México's biggest insurance companies. You can find more details in my ResearchGate and LinkedIn pages.

Research interests

My main research area is probability and adjacent fields. I am particularly interested in stochastic optimal control and differential games, with a focus on mean-field game theory. I have worked in applications of stochastic analysis for point processes such as environmental financial risk and sampling. More recently, I started working in noncommutative (operator-valued) probability and related algebraic structures.

If you are looking to get in contact with me and I have not replied to your first e-mail, please feel free to send a second one.

Publications

Published/Accepted Papers

• Feb. 2026 “Mean-Field Games with common Poissonian noise: A Maximum Principle approach” (with D. Hernández-Hernández), Mathematical Control and Related Fields (Accepted for publication). Preprint available: arxiv.org/abs/2401.10952
• Dic. 2025 “Coupled forward-backward stochastic differential equations with jumps in random environments” (with D. Hernández-Hernández), Stochastic Analysis and Applications, vol. 44, no. 1, pp. 35-64. DOI: 10.1080/07362994.2025.2594452
• Nov. 2025 “Conditional McKean–Vlasov differential equations with common poissonian noise: Propagation of chaos” (with D. Hernández-Hernández), Stochastics and Dynamics, vol. 25, no. 07, p. 2 550 033. DOI: 10.1142/S0219493725500339
• Dec. 2022 “Zero-Sum Stochastic Games with Random Rules of Priority, Discrete Linear-Quadratic Model” (with D. Hernández-Hernández), Dynamic Games and Applications, vol. 12, no. 4, pp. 1293-1311. DOI: 10.1007/s13235-021-00417-9.

Available Preprints

• 2025 “Infinite-Horizon Optimal Control of Jump-Diffusion Models for Pollution-Dependent Disasters” (with D. Sakhanda). Preprint available: 10.48550/arXiv.2511.13568

• 2025 “Branching Stein Variational Gradient Descent for sampling multimodal distributions” (with I. Bañales and A. Jaramillo), Preprint available: 10.48550/arXiv.2506.13916.

Books/Chapters

• 2026 “Optimal Control in Random Environments: Pontryagin Maximum Principle with Environment-dependent Jumps and Mean-Field Games with Common Poissonian Noise,” 2026 (with D. Hernández-Hernández), Springer Briefs in Mathematics (Accepted for publication).

Teaching/Academic experience

• Spring 2026 Seminar on Noncommutative Probability and Random Matrix Theory (Lecturer, Planner). Graduate level Seminar, ETH Zürich.

• Autumn 2025 Topics in Stochastic Optimal Control (Lecturer, Planner). Graduate course in Mathematics, ETH Zürich.

• 2023 Measure theory (Teaching Assistant). Graduate course in Probability and Statistics, CIMAT.

• 2023 Mathematical statistics (Teaching Assistant). Graduate course in Probability and Statistics, CIMAT.

• 2021 Measure theory} (Teaching Assistant). Graduate course in Probability and Statistics, CIMAT.

• 2020 Stochastic modeling in Finance (Teaching Assistant). Graduate course in Probability and Statistics, CIMAT.