Fernando Cordero
Office: UHG U4-151
Phone: +49-521-106-3858
Fax: +49-521-106-6481
Email: fcordero[at]techfak.uni-bielefeld.de
Phone: +49-521-106-3858
Fax: +49-521-106-6481
Email: fcordero[at]techfak.uni-bielefeld.de
Research Interests
My primary research interests are population genetics and mathematical finance. In population genetics, I look at deterministic and stochastic population models that are subject to the evolutionary forces of mutation and selection in its various forms, such as genic selection, frequency-dependent selection, and environmental selection. One of the most recurring and difficult tasks in my research is elucidating the corresponding ancestral structures and establishing formal relationships between forward and backward models. This type of study usually employs methods varying from analytical (relying on the analysis of ordinary, partial or stochastic differential equations), to probabilistic (building on fine properties of discrete or continuous-time Markov processes), and combinatorial (allowing the analysis of finite structures as trees or graphs). In mathematical finance, my research focusses on problems related to the existence and quantification of arbitrage and asymptotic arbitrage in financial markets under friction.Current projects with third-party funding
- Since July 2021 PI in DFG Collaborative Research Centre 1283 Taming uncertainty and profiting from randomness and low regularity in analysis, stochastics and their applications
Education
- Nov. 2020 Habilitation in Mathematics, Faculty of Mathematics, Bielefeld University. Thesis: "Stochastic processes in population genetics and mathematical finance'' Mentor: Ellen Baake.
- 2005-2010 Ph.D. in Applied Mathematics, University Paris VI. Thesis: "On the excursion theory for symmetric stable Lévy processes with index bigger than one and some applications". Supervisors: Frédérique Petit and Marc Yor
- 2004-2005 Master's degree in Probabilities and Applications, University Paris VI. Thesis: "Wiener integrals for Bessel and related processes". Supervisor: Marc Yor
- 1998-2004 Mathematical Engineering, University of Chile. Thesis: "Mathematical analysis of adaptive optics and the command of big telescopes". Supervisor: Jorge San Martín
Professional Career
- Since 2013 Research associate at Bielefeld University (Faculty of Technology)
- 2010-2012 Research associate at the University of Vienna (Faculty of Mathematics)
- 2009-2010 Full-time teaching and research assistant (ATER) at the University Paris VI(Faculty of Mathematics)
- 2008-2009 Half-time teaching and research assistant (ATER) at the University Paris VI (Faculty of Mathematics)
- 2007-2008 Temporary teaching assistant at the University Paris VI (Faculty of Mathematics)
- 2000-2004 Temporary teaching assistant at the University of Chile (Faculty of Mathematics)
Publications and preprints
- F. Cordero, S. Hummel and G. Véchambre. Λ-Wright-Fisher processes with general selection and opposing environmental effects: fixation and coexistence. [arxiv publication]
- P. J. Gerrish, F. Cordero, B. Galeota-Sprung, A. Colato, V. Vejalla, N. Hengartner, P. Sniegowski. Natural selection promotes the evolution of recombination 2: during the process of natural selection. [bioarXiv publication]
- P. J. Gerrish, B. Galeota-Sprung, F. Cordero, P. Sniegowski, A. Colato, N. Hengartner, V. Vejalla, J. Chevallier and B. Ycart. Natural selection and the advantage of recombination. [bioarXiv publication]
- F. Cordero, A. González Casanova, J. Schweinsberg and M. Wilke-Berenguer. Λ-coalescents arising in populations with dormancy. Electron. J. Probab. 27 (9), 1-34. [Journal publication] [arXiv publication]
- F. Cordero and G. Véchambre Moran models and Wright-Fisher diffusions with selection and mutation in a one-sided random environment. [arXiv publication]
- E. Baake, F. Cordero and S. Hummel Lines of descent in the deterministic mutation-selection model with pairwise interaction. Ann. Appl. Probab., in press. [arXiv publication]
- F. Cordero, S. Hummel and E. Schertzer General selection models: Bernstein duality and minimal ancestral structures. Ann. Appl. Probab., in press. [arXiv publication]
- F. Cordero and M. Möhle On the stationary distribution of the block counting process for population models with mutation and selection. J. Math. Anal. Appl., Volume 474, Issue 2 (2019), 1049-1081. [Journal publication] [arXiv publication]
- E. Baake, F. Cordero and S. Hummel A probabilistic view on the deterministic mutation-selection equation: dynamics, equilibria, and ancestry via individual lines of descent. J. Math. Biol., 77 (2018), 795-820. [Journal publication] [arXiv publication]
- F. Cordero, I. Klein and L. Perez-Ostafe Asymptotic arbitrage in the fractional mixed markets. Mod. Stoch Theory Appl., Volume 5, Issue 4 (2018), 415-428. [Journal publication] [arXiv publication]
- F. Cordero The deterministic limit of the Moran model: a uniform central limit theorem. Markov Process. Related Fields, Volume 23, Issue 2 (2017), 313–324. [Journal publication] [arXiv publication]
- F. Cordero Common ancestor type distribution: a Moran model and its deterministic limit. Stochastic Process. Appl., Volume 127, Issue 2, (2017), 590–621. [Journal publication] [arXiv publication]
- F. Cordero and L. Perez-Ostafe Strong asymptotic arbitrage in the large fractional binary market. Math. Financ. Econ., Volume 10, Issue 2 (2016), 179–202. [Journal publication] [arXiv publication]
- F. Cordero, I. Klein and L. Perez-Ostafe Asymptotic proportion of arbitrage points in fractional binary markets. Stochastic Process. Appl., Volume 126, Issue 2 (2016), 315–336. [Journal publication] [arXiv publication]
- F. Cordero The first passage time of a stable process conditioned to not overshoot. J. Theor. Probab., Volume 29, Issue 3 (2016), 776–796. [Journal publication], [arXiv publication]
- F. Cordero and L. Perez-Ostafe Critical transaction costs and 1-step asymptotic arbitrage in fractional binary markets. Int. J. Theor. Appl. Finan., Volume 18, Issue 5 (2015). [Journal publication] [arXiv publication]
- F. Cordero, I. Klein and L. Perez-Ostafe Binary markets under transaction costs. Int. J. Theor. Appl. Finan., Volume 17, Issue 5 (2014). [Journal publication], [arXiv publication]
- F. Cordero On the scaling property in fluctuation theory for stable Lévy processes. Theory Probab. Appl., Volume 55, Issue 4 (2011), 683–691. (Originally published in Teor. Veroyatnost. i Primenen., Volume 55, Issue 4 (2010), 803–812.) [Journal publication], [arXiv publication]
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