75383 - WORKSHOP IN QUANTITATIVE FINANCE

Anno Accademico 2019/2020

  • Docente: Enrico Bernardi
  • Crediti formativi: 6
  • Lingua di insegnamento: Inglese
  • Modalità didattica: Convenzionale - Lezioni in presenza
  • Campus: Bologna
  • Corso: Laurea Magistrale in Quantitative finance (cod. 8854)

Conoscenze e abilità da conseguire

The student is exposed to selected frontier issues of research from scholars in each field. Each scholar will address a topic, starting from the basic principles to the frontier questions. From the workshop, the student will collect ideas for his thesis and interests driving him to his future career.

Contenuti

The course is divided into lectures given by external professors or experts in a field. These are the specific contents this year:

A. Lanconelli

Title

An introduction to the Malliavin Calculus and its applications

Short program

- Motivation: stochastic differential equations and existence of densities
- The Malliavin derivative and Skorohod integral
- Absolute continuity for Brownian functionals
- Absolute continuity for solutions of SDEs
- Financial applications: the Clark-Ocone formula and computation of Greeks

Dr.ssa Elena Bandini, Università di Milano-Bicocca

Title "Optimal control of Piecewise Deterministic Markov Processes"

Summary

The aim of this course is to analyse stochastic models in which the randomness appears as point events, i.e. there is a sequence of
random occurrences at fixed or random times T1 < T2 < T3 •.. but there is no additional component of uncertainty between these times.
We will introduce and study a general class of processes called piecewise-deterministic Markov processes (PDMPs) which are stochastic
models having precisely this property, and sufficiently general to cover a wide variety of applied problems as special cases.
Then we will consider optimal control problems for PDMPs, where a control process acts continuously on the jump dynamics
and on the deterministic flow. For this class of control problems, the value function can be characterized as the unique solution to a partial differential equation called Hamilton-Jacobi-Bellman equation. The value function can as well be described by means of a suitable Backward Stochastic Differential Equation; this latter probabilistic representation, known as nonlinear Feynman-Kac formula, is particularly useful to get numerical approximations of the value function.

Dr. Giovanni Luca Torrisi, CNR-IAC Roma


Titolo: Topics on Hawkes processes

In this mini-course we shall cover the following arguments:

1) A brief introduction on point processes with stochastic intensity

2) Classical Hawkes processes: stability properties and spectra

3) Critical Hawkes processes: stability properties and spectra

4) Applications of Hawkes processes in insurance and/or finance

Testi/Bibliografia

A.Lanconelli

Bibliography

David Nualart, Malliavin calculus and Related Topics, II edition, Springer, New York 2006

Elena Bandini

Davis, M., Markov Models and Optimization, Chapman & Hall/CRC Monographs on Statistics and Applied Probability, 1993.
Bauerle, N., Rieder, U. Markov Decision Processes with Application to Finance, Universitext - Springer, 2011.
Bauerle, N., Rieder, U. Optimal control of Piecewise deterministic Markov processes with finite time horizon, Modern trends of controlled stochastic processes: Theory and Applications, pages 144-160, 2010.

Giovanni Luca Torrisi

D.J. Daley and D. Vere-Jones "An introduction to point processes", Vol. I and II (2003 and 2008, respectively)

Springer, New York

P. Bremaud and L. Massoulie "Stability of nonlinear Hawkes processes", Annals of Probability, 24, 1563-1588, 1996

Metodi didattici

Students might be asked to implement some software on their own devices, i.e. laptops or pcs.

Modalità di verifica e valutazione dell'apprendimento

Attendance is mandatory, at least 75% of all classes is necessary and will be verified. Students will be asked to write a report on each and every one of the lectures.

Strumenti a supporto della didattica

Usual tools in classical theoretical classes.

Orario di ricevimento

Consulta il sito web di Enrico Bernardi