MTH5560 · Partial differential equations for finance

Overview

This unit introduces parabolic partial differential equations (PDEs) with financial applications. Basic solutions concepts and properties will be covered. Connections between PDE and probabilistic formulations will be established via the Feynman-Kac formula. Option pricing theory will be explored via the Black-Scholes equation. The dynamic programming principle and theory of stochastic control will be briefly introduced. You will learn to derive relevant PDEs for financial problems, study their properties, and solve using numerical methods such as finite difference methods, Monte-Carlo methods, and deep learning.

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. Articulate specialised mathematical concepts within the field of partial differential equations;
2. Recognise the complex connections between stochastic analysis and partial differential equations;
3. Apply sophisticated mathematical modelling skills to problems in partial differential equations that relate to financial markets;
4. Demonstrate critical thinking and problem solving skills within the context of financial mathematics;
5. Formulate expert solutions, both analytical and numerical, to practical financial problems using specialised cognitive and technical skills within the field of partial differential equations;
6. Communicate complex information in an accessible format to a non-mathematical audience.

Workload

• 3 hours of seminars; • One hour of applied classes and • 8 hours of independent study per week (including working on assessments and revision)

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