Dr Mauro Mobilia
University Lecturer
Applied Mathematics

                            


                                                                                                                                                     
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           





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Research

Teaching

Teaching qualification: University of Leeds Teaching Award Professional Standard 2
MATH5300M: Applied Financial Modelling (January-May 2012)
Aims and objectives of the course: To provide an introduction to the mathematics of financial derivatives. The course covers the differential equations, stochastic models and quantitative methods needed to understand Black-Scholes formulae. The objectives of this course are:
  1. Recognise ordinary and partial differential equations.
  2. Understand random variables and probability distributions.
  3. Interpret a stochastic differential equation and its solution
  4. Understand the log-normal asset price model used in finance
  5. Use the Ito formula in simple examples
  6. Be familiar with Black-Scholes formula
  7. Understand the no arbitrage principle and its use to calculate a fair price for options 
General information on the course can be found here

Course Resources: Handouts, Questions and Solutions (pdf)


MATH0380: Foundation Applied Mathematics for Business (January-May 2012)

 Syllabus:
- Graphs of linear equations, elimination methods, supply and demand analysis
- Linear programming.
- Percentages, compound interest, discounting, geometric series, calculating the AER
- Addition, subtraction and multiplication of matrices
- The inverse of a matrix
- Evaluation of determinants
- Eigenvalues of a matrix
- Linear difference equations, simple economic models

General information is available here

Course Resources (notes, examples & assignments, solutions):

Chapter 1: Brief notes on Sections 1.1, 1.2, 1.3-1.4 and 1.5  (collated notes)
Chapter 2: Brief notes on Sections 2.1 and 2.2  (collated notes)
Chapter 3: Brief notes on Sections 3.1, 3.2 and 3.3-3.4  (collated notes)
Chapter 4: Brief notes on Sections 4.1-4.2, 4.3-4.4 and 4.5-4.6  (collated notes)
Chapter 5: Brief notes on Sections 5.1-5.2, 5.3, 5.4 and 5.5  (collated notes)
Final advice
Example Sheet 1 Solutions 1
Example Sheet 2 Solutions 2
Example Sheet 3 Solutions 3
Example Sheet 4 Solutions 4
Example Sheet 5 Solutions 5
Example Sheet 6 Solutions 6
Example Sheet 7 Solutions 7
Example Sheet 8 Solutions 8
Example Sheet 9 Solutions 9
Example Sheet 10 Solutions 10
May 2010 exam paper and Check-sheet
May 2011 exam paper and Check-sheet

MATH1610: Discrete Systems (January - May 2009)

Syllabus of MATH1610: Discrete Systems

  • Vector Algebra 
  • One-dimensional Iterated Maps
  • Two-dimensional Iterated Maps

Lectures notes (pdf)

Examples and past exam paper (pdf)