PREPARATORY COURSE

​

Module 1: Probability

​

Objective: Explain some elementary concepts of the mathematical theory of probability. It exposes which are the probability distributions used in financial and insurance risks and how to estimate parameters. The importance of probability in Solvency II is explained.

​

• Introduction to probability

• Combinatorial analysis

• Conditional probability and independence

• Random variables

• Density and distribution functions

• Expectation, variance, moments

• Probability distributions

• Frequency distributions, Poisson, Binomial, Negative Binomial

• Loss distributions, lognormal, EVT, gyh, beta, gamma, weibull, etc.

• Random Vectors

• Distribution fitting and parameter estimation

• Use of probability distributions in Solvency II

• Exercise 1: Probability distribution fits in R

 

Module 2: Statistics

 

Objective: Inferential statistics consists of a set of techniques to obtain, with a certain degree of confidence, information from a population based on information from a sample. Statistics is essential for the construction of models and their validation.

​

• Introduction

• Variables and data types

• Descriptive statistics

• Inferential statistics

• Random samples and statistics

• Point estimate

• Estimation by intervals

• Hypothesis tests

• Importance of statistics in Solvency II

• Exercise 2: Descriptive statistics in Python of data from an insurance company

• Exercise 3: Hypothesis testing in R

​

Module 3: Finance

 

Objective: To review the concepts of the value of money over time, financial mathematics, valuation of annuities, bonds, and valuation models Capital Asset Pricing Model and Arbitrage pricing theory. The models are essential for the valuation of assets and liabilities of an insurance company.

 

• Value of money over time

• Financial mathematics and annuities

• Bond valuation

• Duration and convexity

• CAPM and APT model

• Stochastic processes

• Monte Carlo simulation

• Exercise 4: Valuation of bonds in Excel

• Exercise 5: Estimation of duration and convexity in Excel

• Exercise 6: Estimation of the CAPM and APT in Excel

• Exercise 7: Monte Carlo Simulation and Stochastic Processes in R

​

Module 4: Programming in Python

 

Objective: Explain what the Python programming language is and its functionalities. It explains what Jupyter is and how to install it. Expose basic notions of programming and the libraries that will be used to develop Solvency II models.

 

• Introduction to Python

• Environment and library installation

• Jupyter

• Import and export of data

• basic programming

• statistical tools

• regression libraries

• finance bookstores

• Machine Learning Libraries

• Quantum Libraries

• Exercise 8: Programming in Python

 

Module 5: Programming in R

​

Objective: Explain what R and Rstudio are and how to install them. Explain basic notions of R programming and the libraries used to develop Solvency II models.

 

• Introduction to R

• Environment and library installation

• R Studio

• Import and export of data

• Basic programming

• Statistical tools

• Regression libraries

• Finance bookstores

• Actuarial science bookstores

• Exercise 9: programming in R

​

Module 6: Machine Learning

​

Objective: Automatic machine learning, in English machine learning, essential for systems to be intelligent, allows the development of predictions based on data and improves the projections of traditional models. The use of machine learning and deep learning algorithms is introduced. The benefits of machine learning in risk management for insurance companies are explained.

 

• Introduction Machine Learning

• Differences with statistics

• Supervised and unsupervised models

• decision trees

• Support Vector Machine

• K-means

• Assembly Learning

• Random Forest

• neural networks

• Introduction to ensemble models

• Introduction to Deep Learning

• Exercise 10: Estimation of the Support Vector Machine and Random Forest

• Exercise 11: Deep learning algorithm creation

 

Module 7: Introduction to Financial Risks

​

Objective: Lay the theoretical foundations on the financial risks that impact insurance companies, explain the types of risks and the sources of such risks. Understand the probability and impact of events that trigger financial risk in insurance companies.

 

• What is risk?

• Financial risks in insurance companies

• Probability and Impact

• Sources of financial risks

• Differences between financial and non-financial risks

• Market risk

• Interest rate risk

• Liquidity risk

• Credit risk

• Operational risk

​

Module 8: Actuarial Sciences

​

Objective: Introduction of actuarial sciences for participants without actuarial training. A brief introduction to life and non-life insurance is presented, as well as actuarial mathematics.

 

• What do actuaries do?

• Introduction to Life insurance

• Introduction to Non-Life insurance

• Type of contracts

• Introduction to Life Insurance Reserves

• Introduction to Non-Life Insurance Reserves

• Margin Based Pricing

• Introduction to actuarial mathematics

• Introduction to Life Insurance

• Introduction to Non-Life Insurance

• Exercise 12: Modeling the distribution of the severity and frequency of claims in Excel and R

• Exercise 14: Simulation of the current values of an Annuity of a life annuity.

​

Module 9: Quantum computing and algorithms

​

Objective: Quantum computing applies quantum mechanical phenomena. On a small scale, physical matter exhibits properties of both particles and waves, and quantum computing takes advantage of this behavior using specialized hardware. The basic unit of information in quantum computing is the qubit, similar to the bit in traditional digital electronics. Unlike a classical bit, a qubit can exist in a superposition of its two "basic" states, meaning that it is in both states simultaneously.

​

• Future of quantum computing in insurance

• Is it necessary to know quantum mechanics?

• QIS Hardware and Apps

• quantum operations

• Qubit representation

• Measurement

• Overlap

• matrix multiplication

• Qubit operations

• Multiple Quantum Circuits

• Entanglement

• Deutsch Algorithm

• Quantum Fourier transform and search algorithms

• Hybrid quantum-classical algorithms

• Quantum annealing, simulation and optimization of algorithms

• Quantum machine learning algorithms

• Exercise 15: Quantum operations

​

Module 10: Introduction to quantum mechanics

​

• Quantum mechanical theory

• wave function

• Schrodinger's equation

• statistical interpretation

• Probability

• Standardization

• Impulse

• The uncertainty principle

• Mathematical Tools of Quantum Mechanics

• Hilbert space and wave functions

• The linear vector space

• Hilbert's space

• Dimension and bases of a Vector Space

• Integrable square functions: wave functions

• Dirac notation

• operators

• General definitions

• hermitian adjunct

• projection operators

• commutator algebra

• Uncertainty relationship between two operators

• Operator Functions

• Inverse and Unitary Operators

• Eigenvalues and Eigenvectors of an operator

• Infinitesimal and finite unit transformations

• Matrices and Wave Mechanics

• matrix mechanics

• Wave Mechanics

​

Module 11: Introduction to quantum error correction

​

• Error correction

• From reversible classical error correction to simple quantum error correction

• The quantum error correction criterion

• The distance of a quantum error correction code

• Content of the quantum error correction criterion and the quantum Hamming bound criterion

• Digitization of quantum noise

• Classic linear codes

• Calderbank, Shor and Steane codes

• Stabilizer Quantum Error Correction Codes​

​

​Module 12: Quantum Computing II

 

• quantum programming

• Solution Providers

• IBM Quantum Qiskit

• Amazon Braket

• PennyLane

• cirq

• Quantum Development Kit (QDK)

• Quantum clouds

• Microsoft Quantum

• Qiskit

• Main Algorithms

• Grover's algorithm

• Deutsch–Jozsa algorithm

• Fourier transform algorithm

• Shor's algorithm

• Quantum annealers

• D-Wave implementation

• Qiskit Implementation

• Exercise 16: Grover, Fourier Transform and Shor algorithm simulation

​

Module 14: Quantum Machine Learning

​

• Quantum Machine Learning

• hybrid models

• Quantum Principal Component Analysis

• Q means vs. K means

• Variational Quantum Classifiers

• Variational quantum classifiers

• Quantum Neural Network

  • Quantum Convolutional Neural Network

  • Quantum Long Short Memory LSTM

• Quantum Support Vector Machine (QSVC)

• Exercise 17: Quantum Support Vector Machine

​

Module 15: Quantum computing in insurance companies

​

• Building Blocks of Payoff Valuation

  • Distribution Loading

  • Payoff Implementation

  • Calculation of the Expected Value

• Amplitude Estimation

  • Amplitude Estimation based on Phase Estimation

  • Amplitude Estimation without Phase Estimation

• Grover's Quantum Search Algorithm

• Insurance-related Payoffs

  • Overall Payoff

• Insurance-related Quantum Circuits

  • Whole life insurance

  • Dynamic Lapse

• Quantum Hardware

  • simulator

  • royal hardware

• Exercise 18: Insurance-related Quantum Circuits

​

Module 16: Tensor Networks for Machine Learning

​

• What are tensor networks?

• Quantum Entanglement

• Tensor networks in machine learning

• Tensor networks in unsupervised models

• Tensor networks in SVM

• Tensor networks in NN

• NN tensioning

• Application of tensor networks in credit scoring models

• Exercise 19: Neural Network using Tensor Networks​

​

Module 17: Probabilistic Machine Learning

​​

• Probability

• Gaussian models

• Bayesian Statistics

• Bayesian logistic regression

• Kernel Family

• Gaussian processes

  • Gaussian processes for regression

• Hidden Markov Model

• Markov chain Monte Carlo (MCMC)

  • Metropolis Hastings algorithm

• Machine Learning Probabilistic Model

• Bayesian Boosting

• Bayesian Neural Networks

• Exercise 20: Gaussian process for regression

• Exercise 21: Bayesian neural networks