Dr Angelos Dassios COL6.14

This course is available on the BSc in Actuarial Science. This course is not available as an outside option nor to General Course students.

As numbers might need to be capped if it proves too popular, students from the Statistics and Mathematics departments should be given priority. Given the prerequisites, it is unlikely we will get many students from other departments anyway.

Students must have completed:

EITHER Probability, Distribution Theory and Inference (ST202) OR Probability and Distribution Theory (ST206)

AND Stochastic Processes (ST302).

While the course ST306 is not a formal pre-requisite some examples from this course will be used. Students that have not taken ST306 might have to do a bit of extra reading to familiarise themselves with them.

An introduction to using R for stochastic simulation as well as methods of simulating random variables, complicated quantities involving several random variables and paths of stochastic processes. Applications will focus on examples from insurance and finance.

20 hours of lectures and 10 hours of computer workshops in the LT.

• Introduction to R with an emphasis on stochastic simulation.
• Monte-Carlo integration.
• Generating continuous random variables; inverse distribution function method.
• Generating continuous random variables; acceptance rejection method.
• Generating continuous random variables; sums of random variables.
• Generating continuous random variables; other methods. Normal and Inverse Gaussian distributions.
• Generating discrete random variables.
• Generating the paths of stochastic processes; Insurance loss process; Brownian motion; Ornstein-Uhlenbeck process.
• Various applications in insurance and finance.

There will be a Q&A session on practical issues in week 11.

Weekly exercises usually involving computing.

• Introducing Monte Carlo methods with R (main reference), by G. Robert and G. Casella.

Useful reading:

• Stochastic Simulation, Algorithms and Analysis by S. Asmussen.
• Monte Carlo Methods in Financial Engineering by P. Glasserman.

Exam (50%, duration: 2 hours) in the main exam period.
Project (25%) in the LT.
Project (25%) in the ST.