Bachelor of Science (BSc)

BSc Actuarial Science and Mathematics

  • Duration: 3 years
  • Year of entry: 2025
  • UCAS course code: NG31 / Institution code: M20
  • Key features:
  • Scholarships available
  • Accredited course

Full entry requirementsHow to apply

Fees and funding

Fees

Tuition fees for home students commencing their studies in September 2025 will be £9,535 per annum (subject to Parliamentary approval). Tuition fees for international students will be £34,500 per annum. For general information please see the undergraduate finance pages.

Policy on additional costs

All students should normally be able to complete their programme of study without incurring additional study costs over and above the tuition fee for that programme. Any unavoidable additional compulsory costs totalling more than 1% of the annual home undergraduate fee per annum, regardless of whether the programme in question is undergraduate or postgraduate taught, will be made clear to you at the point of application. Further information can be found in the University's Policy on additional costs incurred by students on undergraduate and postgraduate taught programmes (PDF document, 91KB).

Scholarships/sponsorships

The University of Manchester is committed to attracting and supporting the very best students. We have a focus on nurturing talent and ability and we want to make sure that you have the opportunity to study here, regardless of your financial circumstances.

For information about scholarships and bursaries please visit our undergraduate student finance pages and our Department funding pages .

Course unit details:
Stochastic Processes

Course unit fact file
Unit code MATH27712
Credit rating 10
Unit level Level 2
Teaching period(s) Semester 2
Available as a free choice unit? No

Overview

A stochastic process is a collection of random variables that describe the progression of a non-deterministic system as a function of time.

Stochastic processes are used as modelling tools within a wide range of applications arising virtually in any area of modern science and engineering where randomness plays a role.

The unit aims to present the most important classes of stochastic processes by focusing on the fundamental examples, describing the meaning of their sample paths, and explaining their role in modelling specific science and/or engineering phenomena.

These classes of stochastic processes are of fundamental interest in (i) Mathematical Finance, (ii) Actuarial Science, and (iii) Statistics, in addition to being of interest in themselves as fundamental entities of modern (iv) Probability Theory that provide fascinating connections to (v) Mathematical Analysis.

Syllabus: (with approximate times)
1. Introduction (stochastic process, sample path, increment, marginal
    law, first entry time) [1 week]
2. Random walk (definition, basic properties, marginal law, examples
    of application) [3 weeks]
3. Poisson process (definition, basic properties, marginal law, examples
    of application) [3 weeks] 
4. Wiener process [Brownian motion] (definition, basic properties, marginal
    law, examples of application) [3 weeks] 
5. Stationary process (definition, covariance function, examples of
    application) [1 week] 
 

Pre/co-requisites

Unit title Unit code Requirement type Description
Probability I MATH11711 Pre-Requisite Compulsory
Probability and Statistics 2 MATH27720 Co-Requisite Compulsory

Aims

The unit aims to:

- Present the most important classes of Stochastic Processes by focusing on the fundamental examples, describing the meaning of their sample paths, and explaining their role in modelling specific science and/or engineering phenomena;

- Provide an overview of Stochastic Processes and explain what the students can expect in related directions from the probability-based units in year 3, 4 and beyond.
 

Learning outcomes

  • Define a stochastic process and describe its meaning as a modelling tool of a specific science/engineering phenomenon.
  • Describe the structure of the sample paths of a stochastic process and derive their basic properties.
  • Derive the marginal law of a stochastic process, calculate its expectation/variance, and study its asymptotic behaviour.
  • Define the first entry time of a stochastic process and apply the derived results in a variety of applied settings.

Assessment methods

Method Weight
Written exam 100%

Feedback methods


Summer exam    
2 hours    General feedback provided after exam is marked.
    

Recommended reading

[1] Bass, R. (2011). Stochastic Processes. Cambridge Univ. Press, (390 pp).
[2] Doob, J. L. (1953). Stochastic Processes. John Wiley & Sons, (654 pp).
[3] Jones, P. W. & Smith, P. (2018). Stochastic Processes: An Introduction. Chapman & Hall, (255 pp).
[4] Karlin, S. & Taylor, H. M. (1975). A First Course in Stochastic Processes. Academic Press, (557 pp).

Study hours

Scheduled activity hours
Lectures 11
Practical classes & workshops 11
Independent study hours
Independent study 78

Teaching staff

Staff member Role
Goran Peskir Unit coordinator

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