David Ruiz G.

TEACHING

"We do not inherit the land from our ancestors, we borrow it from our children."

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Math Lecture Notes:

The following lecture notes are divided into two parts: The first part cover topics in Real and Functional Analysis for a first-year Ph.D. in Economics and Finance, and were used while teaching at Bocconi University. The second part covers advanced topics in those fields that interest me the most:
Dynamical Systems: Most of my influence on Dynamical Systems came from Prof. Arnd Scheel at UofM and my advisor in the Math department Prof. Peter Polacik. Hence my notes are heavily influenced by their lectures into the subject. My approach to these notes is to make the topic relevant to the study of economics. There is also some influence from classical textbooks.
Stochastic Integrals (with Jumps): I take a general approach and define the stochastic integral as a Daniell's extension for the mean, taking as primitive an elementary space of integrands. One reason for taking this approach is to develop general results for SDE's, Optimal Control, and Statistics. However, the main reason is for the study of Dynamic and Stochastic Games, with application into Economics and Finance.
- Notes on Logic- Preliminaries: Set Theory, Lattices and the Reals - Lecture Notes 1: Basic Real Analysis & Euclidean Spaces- Lecture Notes 2: Metric Spaces- Lecture Notes 3: Topological Spaces- Lecture Notes 4: Normed Linear Spaces- Lecture Notes 5: Dynamical Systems- Lecture Notes 6: Measure Theory, Integration and Probability Theory- Lecture Notes 7: Stochastic Integration with Jumps.

Bocconi University, Instructor

40312 - Introduction to Mathematics (Graduate): Fall-'18, Fall-'19, Fall-'20.

Reading Groups:

Ph.D. Bocconi University. Spring '19 - Fall '20 (with Prof. Battigalli): Mechanism Design and Epistemic Game Theory.
Ph.D. University of Minnesota. Fall '20 (with Prof. Rahman): Information Design, Strategic Experimentation, and Persuasion.

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