The contents of this class are based on my book “Extreme Financial Risks and Assets Allocation” published by Imperial College Press and coauthored with Christian Walter. The first part of the class offers a broad introduction to infinitely divisible distributions and to Lévy processes. The main distributions and processes are surveyed and their main properties (activity, variation, moments…) are examined. A strong focus is made on Fourier transform methods.
The second part of the class is dedicated to applications. It shows how static and dynamic portfolio choice problems can be solved in the presence of extreme risks (modeled via Lévy processes in the dynamic case). The course also examined the management of risks and the computation of risk indicators such as Value at Risk or Tail Conditional Expectation when extreme risks are considered.