#### SoFiA School will take place in the main room of Pabellón 1 during the mornings (except Wednesday).

#### It contains four courses of 3 hours each one:

#### Course 1: “*Mathematical Modeling of Social Dynamics*“, by Prof. Maxi San Miguel

**Lecture 1**: *Axelrod model of cultural dissemination*

I will address the question of the cultural globalization-polarization transition and the role of social netwrok structure, cultural drift and social network dynamics in the cultural dynamics. I will also discuss the function of mass media in these processes.

**Lecture 2**: *Game theory*

I will review, from a physics perspective, the basic concepts of game theory used in models of collective social phenomena.

#### Course 2: *“Testing theories of cooperation and polarization by means of social experiments and agent-based models”*, by Prof. Andreas Flache

**Lecture 1**: *Sociological Theories and Agent-based Computational Models of Diversity and Polarization in Society*

I will discuss why explaining opinion diversity and polarization is a puzzle for many classical sociological theories of social influence, then discuss how proposed theoretical solutions have been analyzed with agent-based computational models, what are the strong and weak aspects of various approaches, and what are remaining puzzles for future work.

**Lecture 2**: *Testing theories of cooperation and polarization in the Lab*

Building on lecture 1, I will discuss general principles and problems of testing theories about human social behavior in the lab, focusing in particular on the themes of cooperation and polarization. A number of examples will be discussed in more detail, partially building on my own research.

#### Course 3: *“Quantitative methods in finances”*, by Prof. Frédéric Abergel

What is a limit order book?

It is a device that the vast majority of organized electronic markets (all equity, futures and other listed derivatives markets) use to store in their central computer the list of all the interests of market participants. It is essentially a file in a computer that contains all the orders sent to the market, with their characteristics such as the sign of the order (buy or sell), the price, the quantity, a timestamp giving the time the order was recorded by the market, and a host of various market-dependent information. In other words, the limit order book contains, at any given point in time, on a given market, the list of all the transactions that one could possibly perform on this market. Its evolution over time describes the way the market moves under the influence of its participants. In fact, the study of limit order books can provide deep insight into the understanding of the financial market, which is an excellent example of an evolving “complex system” where the different participants collectively interact to find the best price of an asset. A market in which buyers and sellers meet via a limit order book is called an order- driven market. Essentially, three types of orders can be submitted:

– Limit order: an order to specify a price at which one is willing to buy or sell a certain number of shares, with their corresponding price and quantity, at any point in time;

– Market order: an order to immediately buy or sell a certain quantity, at the best available opposite quote;

– Cancellation order: an order to cancel an existing limit order.

Why study limit order books?

It is clear that the study of the empirical properties, as well as the mathematical modelling and numerical simulation, of limit order books, is of paramount importance for the researcher keen on gaining a deep understanding of financial markets. In classical financial econometrics, the data consist in time series of prices of one or several assets, and models are based on the statistical properties of the various quantities one can build from these time series: returns, volatility, correlation… However, in order-driven markets, the price dynamics is controlled by the interplay between the incoming order flow and the order book. The study of the limit order book therefore reveals, as a by-product, the price dynamics. One of the main motivations for the study of limit order books is to understand the extent to which the mechanisms of the order book have an impact on the price dynamics at the microstructure level, and whether this impact remains visible at lower frequencies. Furthermore, the genuine scientific curiosity for this area of research is very definitely enhanced by the rapid growth of algorithmic trading and high frequency trading. Market making strategies, optimal execution strategies, statistical arbitrage strategies, being executed at the individual order level, all require a perfect understanding of the limit

order book.

How to model limit order books?

There are several steps to take when modelling limit order books. Probably, the first one is to select a mechanistic description of the way incoming orders are stored and market orders are executed. This prerequisite is achieved, at least in a stylized form, in all the mathematical models of limit order books, and plays an important role in the

simulation of limit order books, for which realistic matching engines must be developed in order to study trading strategies. The second step, at a more conceptual and scientifically more fundamental stage, consists in choosing a mechanism for the arrival of orders, that is, for the submission of an order of a particular type at a specific date

and time. In the approach proposed by econophysicists, agents are described statistically. In the simplest form along this line of research, the agents are supposed to act randomly. This approach is sometimes referred to as zero-intelligence order book modeling, in the sense that the arrival times and placements of orders of various

types are random and independent, the focus being primarily on the “mechanistic” aspects of the continuous double auction rather than the strategic interactions between agents. Zero-intelligence models of the order book already capture some salient features of real markets, and exhibit interesting, non-trivial mathematical properties. It

is however necessary to depart from this overly simplified approach and study models were agents do interact, at least in a statistical way. Some advanced limit order book models will be studied and presented.

**Lecture 1**: *High frequency order-book data – Survey of stylized facts on limit order books
*

**Lecture 2**: *Experimental evidence of the interaction between agents – The mathematical theory of zero-intelligence models*

** Lecture 3**: *More advanced models for interacting and competing statistical agents.*

#### Course 4: “*From Individual Mobility to Transportation Networks”, *by Prof. Marta González

**Lectures 1 & 2:** *A review of human mobility: basic mechanisms and urban effects*

We will review up to date findings in human mobility. In the first part we cover the mechanisms to model of individual spatial-temporal trajectories that compare with travel diaries. Next we review its implications for modeling trips in the streets and the potential of smart commute apps given realistic congestion scenarios in various cities. We close with future directions and open questions in the area.