Hello and welcome!
(This site is still under construction)
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.
My main research interests are optimal control and stochastic differential games; in particular, I am interested in mean-field game theory, its interactions with optimal transport and backward stochastic differential equations, and its implementation in real-world problems.
Publications
Published/Accepted Papers
- Dec. 2022 (with D. Hernández-Hernández), “Zero-Sum Stochastic Games with Random Rules of Priority, Discrete Linear-Quadratic Model,” Dynamic Games and Applications, vol. 12, no. 4, pp. 1293-1311, ISSN: 2153-0785, 2153-0793. DOI:
10.1007/s13235-021-00417-9[Online]. Available: https://link.springer.com/10.1007/s13235-021-00417-9
Preprints
- 2024 (with D. Hernández-Hernández), “Mean-Field Games with common Poissonian noise: A Maximum Principle approach,” DOI:
10.48550/ARXIV. 2401.10952[Online]. Available: https://arxiv.org/abs/2401.10952 - 2023 (with D. Hernández-Hernández), “Conditional McKean-Vlasov Dif- ferential Equations with Common Poissonian Noise: Propagation of Chaos”, DOI:
10.48550/ARXIV.2308.11564[Online]. Available: https://arxiv. org/abs/2308.11564 - 2023 (with D. Hernández-Hernández), “Coupled forward-backward stochas- tic differential equations with jumps in random environments,” DOI:
10. 48550/ARXIV.2307.14318[Online]. Available: https://arxiv.org/abs/ 2307.14318