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Filtering algorithms for Levy processes, with application to financial modelling


Mathematics

About the Project

The problem of inference about the values of hidden or latent variables from imperfect sensor measurements arises in many branches of science, including engineering and mathematical finance. A typical example would be inferring the position and the velocity of a moving object using imperfect measurements from radar or an optical sensor. The measurements are typically the distance between the sensor and the object and the angle with respect to a reference direction. New measurements are received periodically which are used to update the location and velocity information. Mathematically, this problem is not unlike the problem of estimating volatilities implied by observed prices of financial derivatives. Similar `state estimation’ problems arise elsewhere in physical and mathematical sciences, where one has to deal with equations describing the dynamics of a system involving randomness and a problem of inferring the values of unobserved variables from the values of the observed ones. The technique to deal with this problem is called `filtering’. For systems with complex nonlinear dynamics, filtering remains a difficult problem. The exact nonlinear filter is often impossible to implement and different approximate methods exist to deal with state estimation in nonlinear systems.

The proposed project will address the problem of designing computationally tractable filtering algorithms for a class of nonlinear systems with discontinuous dynamics, which are described by Levy processes. The choice of this class of systems is motivated by the fact that many phenomena in financial markets are modelled well using Levy processes. The algorithms designed will be coded in a high level programming language and will be tested on real data on financial derivative prices. Computational tractability is a major issue when one deals with intra-day price changes, and hence methods for high volume statistical data processing will also be explored for their incorporation into the filtering framework.

The student needs to have a first degree in mathematics, engineering or economics (with a strong maths component), with an interest in finance and financial computing.

Funding Notes

Brunel offers a number of funding options to research students that help cover the cost of their tuition fees, contribute to living expenses or both. See more information here: View Website. Recently the UK Government made available the Doctoral Student Loans of up to £25,000 for UK and EU students and there is some funding available through the Research Councils. Many of our international students benefit from funding provided by their governments or employers. Brunel alumni enjoy tuition fee discounts of 15%.)

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