# Primer on Data Science 2020

# Trento, 12-14 February 2020

# Aim

**Primer on Data Science** is a serie of summer/winter schools organized by the curriculum **Mathematics and Statistics for Life and Social Sciences** of the Laurea Magistrale in Mathematics (Department of Mathematics, University of Trento), to the aim of introducing third year bachelor students and bachelor graduates to the topics of this curriculum. Every year the school will have a different topic.

The 2020 edition will focus on a gentle introduction to some aspects of **Mathematical Finance and Actuarial Statistics**.

Lectures will be delivered in English.

# Where

Activities are in rooms A206 and A207 of Polo Scientifico e Tecnologico “Fabio Ferrari”, Povo 1, see here

# Admission

## Students

The school is open to 30 participants, no fees are required, but registration is mandatory. Everybody is welcome to apply, however, admission will be based on the following criteria in order of importance

- Bachelor graduates and third year bachelor students in Mathematics
- Transcript of Records and grades
- Students from University of Trento

**Application is open**

please go here

## PhD Students

The school is open to 10 participants, no fees are required, but registration is mandatory. Everybody is welcome to apply, however, admission will be based on the following criteria in order of importance

- PhD Students from University of Trento

**Application is open**

please go here

## Professionals

PDS2020 is also open to professionals and companies: for further information (fee, registration form etc) please contact Francesca Stanca.

## Participation in the school includes

- Access to the material: notes, slides, videos of the courses
- Coffee breaks
- Access to the university canteen (lunch time)

# Lectures

**Ermanno Pitacco**(Università di Trieste)

Ermanno Pitacco is full professor of Actuarial Mathematics and Life Insurance Technique in the University of Trieste, and academic director of the Master in Insurance and Risk Management in the MIB School of Management in Trieste.

He is an actuary and a member of several actuarial associations and committees, among which the Actuarial Association of Europe, the AFIR/ERM Section of the International Actuarial Association (ICA) and the Mortality Working Group of the ICA. He is editor of the Springer Actuarial Series, and coeditor or associate editor of several journals in the field of actuarial mathematics and insurance. Main fields of scientific interest are: life and health insurance mathematics, longevity risk, portfolio valuations.

He authored or co-authored papers and textbooks in the field of actuarial mathematics and actuarial techniques.

He was awarded with the 1996 INA prize for Actuarial Mathematics from Accademia Nazionale dei Lincei, and the 2011 Bob Alting von Geusau Memorial Prize, together with Annamaria Olivieri, for the best paper published in the ASTIN Bulletin on an AFIR related topic: “Stochastic Mortality: the Impact on Target Capital”. More details can be found at www.ermannopitacco.com.

**Giovanni Alessandro Zanco**(LUISS Guido Carli)

He obtained the High School Diploma in classical studies and a Music Diploma in Milan, before studying Mathematics at the University of Milano-Bicocca, where he got Bacherlor’s and Master’s degree with a thesis on stochastic control under partial information, advisor Prof. Gianmario Tessitore. He obtained the PhD from the Galilei School of the University of Pisa in 2015 under the direction of Prof. Franco Flandoli, with a thesis about parabolic path-dependent PDEs and stochastic calculus tools in Banach spaces. After three years as a PostDoc in the Stochastic Analysis group of the Institute of Science and Technology Austria, led by Prof. Jan Maas, he became researcher at Luiss Guido Carli in 2018. His research concerns: stochastic analysis in infinite dimensions, in particular path-dependent PDEs, Ito formulae in Banach spaces, regularity issues for functions with memory; critical stochastic PDEs; continuous limits of interacting systems and their application to neuroscience; mean field games with applications to micro and macro economic models.

**Paolo Pigato**(Roma Tor Vergata, Department of Economics and Finance)

Paolo Pigato works at the department of Economics and Finance of Rome-Tor Vergata University. Previously he was a postdoctoral researcher at WIAS Berlin, in the research group Stochastic Algorithms and Nonparametric Statistics, and at Inria Nancy-Grand Est, in the TOSCA team. He obtained his PhD in mathematics in 2015 from Universita di Padova and Universite Paris-Est. More details can be found at sites.google.com/site/pigatop.

# Program

## Day 1 (12/02/2020)

- [13:00- ] Registration Desk is open
- [13:45-14:00] Welcome

### A lesson from actuarial mathematics: “be stochastic but also, from time to time, reasonably deterministic” (Part 1)

Room A206 [14:00-15:30] [16:00-17:30]

**Ermanno Pitacco** (Università di Trieste)

- Introduction and Motivation
- Once upon a time: the “traditional” actuarial mathematics
- Awareness of “risk”

### Material

## Day 2 (13/02/2020)

### A lesson from actuarial mathematics: “be stochastic but also, from time to time, reasonably deterministic” (Part 2)

Room A206 [8:30-10:00]

**Ermanno Pitacco** (Università di Trieste)

- Risk assessment in life insurance: pioneering contributions
- ERM: a new road map
- Concluding remarks

### Material

### Systems with controls and interaction: mean field games and economic geography

Room A206 [10:30-12:00] [14:00-15:30] [16:00-17:30]

**Giovanni Alessandro Zanco** (LUISS Guido Carli)

I will give an informal introduction to stochastic dynamics and integration and to the theory of controlled stochastic equations. The goal is to motivate, at least intuitively, the appearence of systems of PDEs usually referred to as mean field games as a convenient tool to analyse the behaviour of economic agents that interact with each other. After introducing the economic situation we want to study, we will discuss the mathematical tools that allow to model it as a system of differential equations, and then try to understand the role of the control on the dynamics of the model. We will finally introduce the tools of stochastic calculus that allow to understand the behavior of our model using partial differential equations: this intuitively corresponds to considering an infinite number of interacting agents.

### Material

## Day 3 (14/02/2020)

### An introduction to mathematical option pricing

Room A207 [9:00-10:30] [11:00-12:30] [14:00-15:30]

**Paolo Pigato** (Roma Tor Vergata, Department of Economics and Finance)

- Options
- Pricing European vanilla options
- The Binomial tree method
- The Black-Scholes model
- Historical vs Implied volatility
- Some stylized facts

### References

- J. Hull: Options, Futures, and other Derivatives (many editions)
- O. Pironneau and Y. Achdou. Computational Methods for Option Pricing (2005)
- S. E. Shreve. Stochastic Calculus for Finance I: The Binomial Asset Pricing Model (2004)

### Material

# Organizers

- Claudio Agostinelli (claudio.agostinelli@unitn.it)
- Stefano Bonaccorsi (stefano.bonaccorsi@unitn.it)
- Carlo Orrieri (carlo.orrieri@unitn.it)

# Information

In case you need more information you can contact Stefano Bonaccorsi (stefano.bonaccorsi@unitn.it).