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MA50299: Risk, randomness and optimisation

[Page last updated: 09 August 2024]

Academic Year: 2024/25
Owning Department/School: Department of Mathematical Sciences
Credits: 6 [equivalent to 12 CATS credits]
Notional Study Hours: 120
Level: Masters UG & PG (FHEQ level 7)
Period:
Semester 1
Assessment Summary: EXCB 100%
Assessment Detail:
  • Examination (EXCB 100%)
Supplementary Assessment:
Like-for-like reassessment (where allowed by programme regulations)
Requisites:
Learning Outcomes: Apply a range of mathematical optimisation algorithms and processes. Assess the strengths and weaknesses of specific algorithms or approaches.
Apply mathematical knowledge to solve quantitative problems arising in financial applications.
Assess and explain to a non-specialist the risk associated to specific random outcomes.
Perform a range of mathematical and statistical computations to solve problems in probability and statistics.


Synopsis: This unit will provide you with a solid background in the mathematical concepts and methods that will be important elsewhere in the programme. Particular emphasis will be placed on relevant concepts in probability, statistics and optimisation. The content will be discussed in the context of a range of important applications in Finance such as utility maximisation, risk management, and insurance.

Aims: This unit will provide students with a solid background in the mathematical concepts and methods that will be important elsewhere in the programme. Particular emphasis will be placed on relevant concepts in probability, statistics and optimisation. The content will be discussed in the context of a range of important applications in Finance such as utility maximisation, risk management, insurance etc.

Skills: Problem solving (T, F, A) Mathematical fluency (T, F, A) Communication of risk (T, F, A) Mathematical and statistical modelling (T, F, A)

Content: Probability: random variables, mean, variance, correlation and covariance, Markov chains. Statistics: basic hypothesis testing, Bayesian vs classical approaches, linear and multiple regression, maximum likelihood estimators. Optimisation: Lagrangian methods. linear, quadratic, convex and non-linear programming and KKT conditions. Local vs global maxima. Gradient descent. Linear regression as a minimisation problem. Applications: utility theory. Measures of risk (value at risk, expected shortfall). Copulas for modelling dependence of financial risks. Reinsurance. Communication of financial risks.

Course availability:

MA50299 is Compulsory on the following courses:

Department of Mathematical Sciences

Notes:

  • This unit catalogue is applicable for the 2024/25 academic year only. Students continuing their studies into 2025/26 and beyond should not assume that this unit will be available in future years in the format displayed here for 2024/25.
  • Courses and units are subject to change in accordance with normal University procedures.
  • Availability of units will be subject to constraints such as staff availability, minimum and maximum group sizes, and timetabling factors as well as a student's ability to meet any pre-requisite rules.
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