units

MTH5210

Faculty of Science

18 September 2017 22 December 2024

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This unit entry is for students who completed this unit in 2016 only. For students planning to study the unit, please refer to the unit indexes in the the current edition of the Handbook. If you have any queries contact the managing faculty for your course or area of study.

Monash University

6 points, SCA Band 2, 0.125 EFTSL

Postgraduate - Unit

Refer to the specific census and withdrawal dates for the semester(s) in which this unit is offered.

Faculty

Science

Organisational Unit

School of Mathematical Sciences

Coordinator(s)

Professor Fima Klebaner

Offered

Clayton

  • First semester 2016 (Day)

Synopsis

Variations and quadratic variation of functions. Review of integration and probability. Brownian motion. Ito integrals and Ito's formula. Stochastic differential equations and diffusions. Calculation of expectations and PDE's, Feynman-Kac formula. Martingales and semimartingales. Change of probability measure and Girsanov theorem. Fundamental theorems of asset pricing. Change of numeraire. Application to options.

Outcomes

On completion of this unit students will be able to:

  1. Develop specialised mathematical knowledge and skills within the field of stochastic calculus.
  2. Understand the complex connections between financial and probabilistic concepts.
  3. Apply sophisticated stochastic modelling skills within the context of financial markets.
  4. Apply critical thinking to problems in stochastic calculus and financial mathematics.
  5. Apply problem solving skills within the finance context.
  6. Formulate expert solutions to practical financial problems using specialised cognitive and technical skills within the field of stochastic calculus.
  7. Communicate complex information in an accessible format to a non-mathematical audience.

Assessment

Weekly homework: 10%
Assignments: 10%
Minor project: 10%
Exam: 70%

Workload requirements

Two 1.5-hour lectures and one 1-hour tutorial per week

See also Unit timetable information

Chief examiner(s)

Professor Fima Klebaner

Prerequisites

MTH3241 (or equivalent) and MTH3251 (or equivalent)

Co-requisites

Only students enrolled in the Master of Financial Mathematics can enrol in this unit. Exceptions can be made with permission from the unit co-ordinator.