Scheda insegnamento

Anno Accademico 2018/2019

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.


Il corso consiste di più moduli tenuti da docenti esterni.


Giovanni Della Lunga: Copula and Montecarlo Simulation for Finance: A Computational Approach

One of the design decisions for a Monte-Carlo simulation is a choice of probability distributions for the random inputs. Selecting a distribution for each individual variable is often straightforward, but deciding what dependencies should exist between the inputs may not be. Ideally, input data to a simulation should reflect what is known about dependence among the real quantities being modelled. In these lessons, after a short theoretical introduction, we show how to use copulas in practical situation to generate data from multivariate distributions when there are complicated relationships among the variables, or when the individual variables are from different distributions


Nikola Gradojevic: Artificial Intelligence (AI) and its applications in the
finance industry

We have witnessed a rapid expansion of AI such as
artificial neural networks and fuzzy logic controllers in the finance
industry in recent years. Its use is expanding because of
improvements in technology, deregulation of markets and increased
competition. While AI systems are making the work of finance
professionals easier, they are still supervised by humans and thus
prone to errors that may potentially pose risks to the industry. This
seminar will discuss both benefits and threats of the use of AI
in the finance industry.





The tutorial aims to provide the attendees with a general overview and some examples of applications of most relevant machine learning techniques to actuarial science, especially in non-life pricing. The tutorial will be split into two parts, a theoretic introduction, and an application section.
The theoretic introduction will:

-introduce students to big - data concepts;

-describe in general the machine learning workflow;

-briefly explain key supervised learning methods;

-briefly explain key unsupervised learning methods;

The application section will present four examples on:

-unsupervised classification applied to vehicle data for MTLP pricing;

-comparison of logistic regression vs machine learning methods to predict corporate bankrupcies;

-gradient boosting methods vs glm to predict severity;

-machine learning explanation (DALEX and LIME).ᐧ


Pietro Rossi: Introduction to Credit Risk Modelling

This talk is geared towards providing the essential elements needed to understand the talk: "Credit risk modeling in practice: an introduction to regulatory and modeling aspects".
We will review basic concepts concerning Credit Risk and commonly used modeling assumptions. The survey will cover item like default probabilities, loss given default "LGD", Merton and reduced models.


Francesco Nisi: Credit risk modeling in practice: an introduction to regulatory and modeling aspects

Financial institutions are asked to estimate credit risk parameters for both business and regulatory needs. Each of these applications has its own modeling requirements.
In this talk we will review the main aspects of real-world credit risk modeling including PD and LGD estimation as well as the related accounting rules to be fullfiled (IFRS 9).
In particular we will focus on the model developed by Prometeia for computing lifetime probabilities of default to be used for IFRS 9, ICAAP and Stress Testing purposes.






For the Lecture on "Copula and Montecarlo Simulation for Finance: A Computational Approach":

1) For copula theory

  • U. Cherubini et al. ”Copula Methods in Finance”, Wiley Finance, 2013

  • Embrechts ”Copulas a Personal View” Working Paper

  • Embrechts et al. ”Modelling Dependence with Copulas and Application to Risk Management”, Department of Mathematik, ETHZ, Zurich, working paper

  • Embrechts et al. ”Correlation and Dependency in Risk Management: Properties and Pitfalls”, Department of Mathematik, ETHZ, Zurich, working paper

  • Lindskog ”Linear Correlation Estimation”, RiskLab ETH, working paper

  • Nelsen ”An Introduction to Copulas”, Lecture Notes in Statistics, Springer-Verlag, 1999

  • Scarsini ”On Measures of Concordance”, Stochastica, 8, 201-208

2) For Montecarlo:

  • Damiano Brigo, Fabio Mercurio ”Interest Rate Models — Theory and Practice” Springer Finance (2006)

  • Damiano Brigo, Massimo Morini, Andrea Pallavicini ”Counterparty Credit Risk, Collateral and Funding” Wiley Finance (2013)

  • Yves Hilpisch ”Derivatives Analytics with Python” Wiley Finance (2015)

  • Don L. McLeish ”Monte Carlo Simulation and Finance” Wiley Finance (2005)

For the Lecture on "Artificial Intelligence (AI) and its applications in the
finance industry

  • Thomas Fischer, Christopher Krauss, (2018), Deep learning with long short-term memory networks for financial market predictions, European Journal of Operational Research, 270 (2), pp. 654–669.
  • Gradojevic N., Gencay R., (2013), Fuzzy Logic, Trading Uncertainty and Technical Trading, Journal of Banking & Finance, 37(2), pp. 578–586.
  • Gradojevic N., Gencay R., Kukolj D., (2009), Option Pricing with Modular Neural Networks, IEEE Transactions on Neural Networks, 20(4), pp. 626-637.
  • Salim Lahmiri, Stelios Bekiros, (2019), Cryptocurrency forecasting with deep learning chaotic neural networks, Chaos, Solitons & Fractals, 118, pp. 35–40,
  • Yong Hu, Kang Liu, Xiangzhou Zhang, Lijun Su, E.W.T. Ngai, Mei Liu, (2015), Application of evolutionary computation for rule discovery in stock algorithmic trading: A literature review, Applied Soft Computing, 36, pp. 534–551.


    1. Applied Predictive Modeling Kuhn, Max and Johnson, Kjell 2013 Springer

    2. Keras, Chollet, François, 2015


For the Lecture on: "Introduction to Credit Risk Modelling":

Black, Fischer and Myron S. Scholes.
The pricing of options and corporate liabilities,
Journal of Political Economy, 81, (1973) 637-654.

Merton, Robert C. (1970).
A dynamic general equilibrium model of the asset market
and its application to the pricing of the capital structure
of the firm,
unpublished manuscript. Available in Merton (1990).

Merton, Robert C. (1974).
On the pricing of corporate debt: the risk structure
of interest rates,
Journal of Finance, 29, 449-470. Available in Merton (1990).

DUFFIE, Darrell; SINGLETON, Kenneth J.
Credit risk: pricing, measurement, and management.
Princeton University Press, 2012.


For the Lecture on: "Credit risk modeling in practice: an introduction to regulatory and modeling aspects":

The Basel II risk parameters
(scaricabile da:
http://www.hkfrm.org/resources/Risk_Parameters.pdf ), cap. 1, 2, 3, 8, 9.

An Explanatory Note on the Basel II IRB Risk Weight Functions
(scaricabile da: https://www.bis.org/bcbs/irbriskweight.pdf )

IFRS9 - project summary
(scaricabile da:

Credit risk analytics - measurement techniques, applications and
examples in SAS and R (http://www.creditriskanalytics.net/ )

Carlehed, M; Petrov, A.
A methodology for point-in-time–through-the-cycle probability of
default decomposition in risk classification systems.
Journal of Risk Model Validation, 6(3), 2012.

Engle, R.; Granger, C.
Co-integration and error correction: Representation, estimation and
Econometrica, 55(2), 1987.



Metodi didattici

Lezioni frontali. Per quanto riguarda i moduli "Copula and Montecarlo Simulation for Finance: A Computational Approach" e "INTRO TO ML FOR ACTUARIAL SCIENCE" si suggerisce agli studenti di avere un proprio leptop per le implementazioni numeriche.

Modalità di verifica dell'apprendimento

La frequenza è obbligatoria e verrà accertata. Verrà richiesto inoltre di preparare un elaborato su uno dei moduli a scelta.

Strumenti a supporto della didattica


Orario di ricevimento

Consulta il sito web di Sabrina Mulinacci