MTH5210 · Stochastic calculus and mathematical finance

Overview

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.

Offerings

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

The Handbook lists no prerequisite, corequisite or prohibition for this unit.

Learning outcomes

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.

Workload

• Two 1.5-hour seminars; • One 1-hour applied class (in weeks 2-12) and • Eight hours of independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.