## ST302Half UnitStochastic Processes

This information is for the 2021/22 session.

Teacher responsible

tbc

Availability

This course is compulsory on the BSc in Actuarial Science. This course is available on the BSc in Business Mathematics and Statistics, BSc in Financial Mathematics and Statistics, BSc in Mathematics with Economics and BSc in Mathematics, Statistics and Business. This course is available as an outside option to students on other programmes where regulations permit and to General Course students.

Pre-requisites

Students must have completed either Probability, Distribution Theory and Inference (ST202) or Probability and Distribution Theory (ST206).

Course content

A second course in stochastic processes and applications to insurance. Markov chains (discrete and continuous time), processes with jumps; Brownian motion and diffusions; Martingales; stochastic calculus; applications in insurance and finance. Content: Stochastic processes in discrete and continuous time; Markov chains: Markov property, Chapman-Kolmogorov equation, classification of states, stationary distribution, examples of infinite state space; filtrations and conditional expectation; discrete time martingales: martingale property, basic examples, exponential martingales, stopping theorem, applications to random walks; Poisson processes: counting processes, definition as counting process with independent and stationary increments, compensated Poisson process as martingale, distribution of number of events in a given time interval as well as inter-event times, compound Poisson process, application to ruin problem for the classical risk process via Gerber's martingale approach; Markov processes: Kolmogorov equations, solution of those in simple cases, stochastic semigroups, birth and death chains, health/sickness models, stationary distribution; Brownian motion: definition and basic properties, martingales related to Brownian motion, reflection principle, Ito-integral, Ito's formula with simple applications, linear stochastic differential equations for geometric Brownian motion and the Ornstein-Uhlenbeck process, first approach to change of measure techniques, application to Black-Scholes model. The items in the course content that also appear in the content of ST227 are covered here at greater depth. However, ST227 is not a pre-requisite for this course.

Teaching

This course will be delivered through a combination of classes and lectures totalling a minimum of 29 hours across Michaelmas Term. This year, some  of this teaching may be delivered through a combination of virtual classes and flipped-lectures delivered as short online videos. This course includes a reading week in Week 6 of Michaelmas Term.

Formative coursework

Compulsory written answers to two sets of problems.

R Durrett, Essentials of Stochastic Processes; T Mikosch, Elementary Stochastic Calculus with Finance in View; Institute of Actuaries core reading notes.

Assessment

Exam (100%, duration: 3 hours) in the January exam period.

Course selection videos

Some departments have produced short videos to introduce their courses. Please refer to the course selection videos index page for further information.

Student performance results

(2018/19 - 2020/21 combined)

Classification % of students
First 37.1
2:1 27
2:2 15.6
Third 11.7
Fail 8.6

Important information in response to COVID-19

Please note that during 2021/22 academic year some variation to teaching and learning activities may be required to respond to changes in public health advice and/or to account for the differing needs of students in attendance on campus and those who might be studying online. For example, this may involve changes to the mode of teaching delivery and/or the format or weighting of assessments. Changes will only be made if required and students will be notified about any changes to teaching or assessment plans at the earliest opportunity.

Key facts

Department: Statistics

Total students 2020/21: 134

Average class size 2020/21: 45

Capped 2020/21: No

Value: Half Unit

Guidelines for interpreting course guide information

Personal development skills

• Problem solving
• Application of numeracy skills
• Specialist skills