STA 2536 – Data Science for Risk Modelling

Important

This course has restricted enrollment, please contact me if you are interested in taking the course.

Outline:

This course focuses on data science techniques for risk modelling stemming from finance and insurance, including probability and stochastic loss models, maximum likelihood estimation, expectation maximization, generalized linear model and predictive modelling, stochastic claim reserving, Bayesian statistics and credibility theory.


Aggregate Claim Modeling

  • Individual claims
  • Some parametric models
  • Simulation
  • Compound Poisson Models

Estimation

  • Point and interval estimates
  • moment matching, percentile matching
  • Maximum likelihood estimators
  • Fisher Information

Model Selection

  • Graphical methods
  • Hypothesis Testing
  • p-values
  • Likelihood ratio test
  • Kolmogorov-Smirnoff test

Classification

  • Bayes classifier
  • Multi-class logistic regression
  • mixture models

Expectation Maximization

  • completed data log-likelihood
  • general theory

Mixture Models

  • discrete mixture models
  • Gamma mixtures
  • Gaussian mixtures
  • model selection with AIC/BIC

Hidden Markov Models

  • forward-backward algorithm
  • Discrete visible layer
  • Gaussian visible layer
  • model selection with AIC/BIC

Generalized Linear Models

  • Estimation and Fisher scoring
  • Stochastic gradient descent and mini-batch
  • Logistic and Poisson regression

Generalized Additive Models

  • basis expansions
  • spline smoothing
  • Estimation

Jupyter Notebooks < click

Textbook:

The following are recommended (but not required) text books for this course:

  • Loss Models: from Data to Decisions, Klugman, Panjer, & Willmot, John Wiley & Sons
  • The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Hastie,‎ Tibshirani,‎ Friedman, Springer

Location

Tutorials: Thurs 1pm – 3pm in EW 409 ( Stewart building)

Lectures: M on 10am – 1pm in EW 409 ( Stewart building)

Grading Scheme:

Item Frequency Grade
Mini Reports 3 / term 3 x 20%
Main Report 1 / term 20%
Main Presentation 1 / term 20%

All coding work is to be done in Python, and you should use Jupyter notebooks for generating any parts of the report that require coding.

Tutorials:

Your TA is Arvind Shrivats, a Ph.D. student in the Department of Statistical Sciences focusing on research in Financial Mathematics.

Tutorials are held weekly on Thursdays from 1 pm – 3 pm  in Stewart 409 .

Academic Code of Conduct

Below is a link to the academic code of conduct at the University of Toronto:

http://www.utoronto.ca/academicintegrity/index.html