About me

I am a Postdoctoral Assistant Professor at the University of Michigan. My mentors are Prof. Erhan Bayraktar and Prof. Ibrahim Ekren. Prior to that, I was a PhD student at Illinois Tech, advised by Prof. Sergey Nadtochiy. 

Research Interests

Stochastic Control, Contract Theory, Mean Field Games, Machine Learning, Financial and Actuarial Mathematics.

Research papers and publications:

1. G. A. Alvarez, E. Bayraktar, I. Ekren "Contracting a crowd of heterogeneous agents".Submitted for publication, ArXiv preprint arXiv:2507.09415  

2. G. A. Alvarez, I. Ekren, A. Krastios, X. Yang. "Neural operators can play dynamic Stackelberg games". Submitted for publication, ArXiv preprint arXiv:2411.09644 

3. G. A. Alvarez, E. Bayraktar, I. Ekren, L. Huang "Sequential optimal contracting in continuous time". Frontiers of Mathematical Finance, 2025, 4: 114-139, www.aimsciences.org/article/doi/10.3934/fmf.2025001 

4. G. A. Alvarez, S. Nadtochiy. "Optimal contract design via relaxation: application to the problem of brokerage fee for a client with private signal". To appear in Finance and Stochastics,  ArXiv preprint arXiv:2307.07010.

5. G. A. Alvarez, S. Nadtochiy, and K. Webster “Optimal brokerage contracts in Almgren-Chriss model with multiple clients". SIAM Journal on Financial Mathematics 14 (3), 855-878, ArXiv preprint arXiv:2204.05403. 

Teaching

Fall 2023. MATH 472 - Numerical Analysis with Financial Applications. University of Michigan. Two sections. 

Winter 2024. MATH 474 - Introduction to Stochastic Analysis with Financial Applications. University of Michigan.

Fall 2024. MATH 472 - Numerical Analysis with Financial Applications. University of Michigan. Two sections.

Winter 2025. MATH 574 - Continuous Time Mathematical Finance. University of Michigan.

Fall 2025. MATH 472 -  Numerical Analysis with Financial Applications. University of Michigan. Two sections. 

Undergraduate Mentoring 

1. Winter 2025. "Optimal Stopping Problems with Applications to Finance" (co-supervised with Yuqiong Wang). University of Michigan. Final project

Student team: Carlos Rosales, Eren Buyukbozkirli, Sarah Semko, Sijia Wang, Xinran Du.

Awards

1. Allen Shields Outstanding Postdoctoral Professor Teaching Award in Mathematics. University of Michigan, 2025.

2. Best PhD thesis in Applied Mathematics. Illinois Tech, 2023.

3. College of Computing Excellence in Teaching Assistance Award. Illinois Tech, 2023.

Recent Talks:

1. SIAM Conference on Financial Mathematics and Engineering, Miami, July 2025

2. Byrne B2A2 Conference, University of Michigan, June 2025

3. AMS Eastern Sectional Meeting, Hartford (Connecticut), April 2025 

4. Joint Mathematics Meeting, Seattle, January 2025

5. Seminar on Mathematical Finance at the University of Michigan, December 2024. 

6. Peter Carr Memorial Conference, University of Maryland, November 2024