PDEs for Financial Mathematics (online)

The aim of the course is to study the three main types of partial differential equations: parabolic (diffusion equation), elliptic (Laplace equation), and hyperbolic (wave equation), and the techniques of solving these for various initial and boundary value problems on bounded and unbounded domains. Applications and examples, such as the solution technique for Black-Scholes option pricing, will be discussed throughout the course.

Course Information

Most modules require a 2.2 degree in a related discipline or equivalent professional experience. Should you have any queries regarding your eligibility, please contact us at info@advancecentre.ie

N.B. Required honours undergraduate degree (Level 8) a 2:1 (or equivalent grade) BSc in Financial Mathematics, Mathematics, Applied and Computational Mathematics, or Statistics.

On completion of this module learners will be able, but not limited to:

  • Explain the terms existence, uniqueness and stability for PDEs and how this relates to initial and boundary conditions, and explain the difference between Dirichlet and Neumann boundary conditions
  • Determine whether a PDE is linear, nonlinear, homogeneous, inhomogeneous for given examples and solve first order PDEs using the method of characteristics and classify a second order PDE by type (Hyperbolic, Elliptic, Parabolic) and classify it by order or linearity
  • Complete (given a partial proof) proofs for uniqueness of solutions for the wave, diffusion and Laplace equations
  • Demonstrate the use of energy methods and the maximum principle to determine uniqueness and stability for a given PDE.
  • Construct finite difference formulations for diffusion equation and Laplace equation, Fourier series expansions for a given periodic function, and half period expansions, both sine and cosine.
  • Apply the method of separation of variables to solve the diffusion equation, wave equation and Laplace equation with both Dirichlet and Neumann conditions.
  • Complete in clearly argued mathematics (given a partial proof) the proof of convergence of Fourier series. This includes the Riemann Lebesque Lemma.
  • Determine the Fourier transform of basic functions, and determine the Fourier transform of a derivative and the convolution of two functions. Apply the Fourier transform to the diffusion equation and interpret the solutions generated.
  • Model the pricing of a European option by providing a commentary on the Black-Scholes equation. Reduce the Black-Scholes equation to the diffusion equation and solve for a call and put option

Learn from world renowned academic staff in Ireland’s leading, future focused and globally recognised colleges.

Gain an accredited NFQ qualification/micro credential that you may count towards a full award if you so wish in the future.

Previous modules may be used as recognition of prior learning towards Advance Centre degree programmes.

Equip yourself with the latest in demand skillset, tools, know-how and knowledge to succeed in your career.

Gain a competitive edge, influence growth and steer strategic goals in your organisation upon completion of your studies with the Advance Centre.

Yes, if you complete this module it can be credited as part of the MSc Financial Mathematics Full Time or MSc Financial Mathematics Part Time.

Detailed Course Information

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