Stochastic Processes

This module provides an introduction to the theory of stochastic processes that are of frequent use in actuarial science and mathematical finance. Topics covered include:

• Introduction to stochastic processes: filtered probability spaces, martingales, Markov processes
• Brownian motion and continuous stochastic calculus
• Continuous time Markov processes: discrete and continuous state
• Lévy processes
• Point processes and discontinuous stochastic calculus
• Jump-diffusion processes
• Actuarial and financial applications