SOR3012: Stochastic Processes and Risk
The theory of stochastic process is used to model the future behavior of systems in fields ranging from finance to weather forecasing. In stochastic models the future behavior of the system is modelled using random variables and probability. One can thus obtain information on the likelihood that the future will transpire in a particular way. In this module we focus primarily on probabilistic models that have the Markov property. In these models the probability of the future transpiring in a particular way depends only on the present state of the system and not on what happened in the past. These models find application in physics, quantitative finance and machine learning. A particularly important application of Markov processes is the method of Monte Carlo integration. We will thus finish by studying this technique and its application to problems in Bayesian inference.
The module assessment consists of the following activities:
|One two page report on random variables||16:00 Tuesday Week 4||10|
|One portfolio of work done during the semester||16:00 Tuesday Week 13 (1st week of second semester)||45|
|One three hour examination in which all questions on the paper must be answered||April exam period||45|
Details on what you are expected to work on during each week of the semester can be found by clicking here .
A summary of some of the key ideas and theorems that are introduced in this module can be found by clicking here .
The final aspect of the assessment for this module is a portfolio for which you must produce projects on the following:
- Random variables
- The central limit theorem
- Markov chains in discrete time
- Markov chains in continuous time
Details on how your final portfolio will be assessed can be found by clicking here .
Some questions to think about when writing your weekly reports can be found by clicking here .