Research

I work as part of the Mathematical Modelling in Finance and Economics Group in which we model financial systems with uncertain price and uncertain physical flow, leading to non-linear PDEs which must be solved numerically. I have investigated such systems in the world of mining, working with the international leading mining software company Gemcom, and also within the framework of Revenue Management systems, working with the local business Inventive IT. If you are interested in a PhD or want to know a bit more then head over to the Mathematical Finance page in MIMS.

Teaching

I currently teach MATH60082 Computational Finance to MSc students and the popular second year course MATH20912 Introduction to Financial Mathematics. I run introductory courses for the postgrad students on Unix, Latex and using the NAG library, and have in the past given courses on Fortran, C++, matlab and gnuplot. Notes, examples and lectures are all available in the teaching section of my website.

Personal

I've been living in Manchester now for nearly fifteen years, completing my BSc, MSc, PhD and post doc work in the department. In my spare time I play football for AFC Didsbury in the Manchester Amateur Sunday League, and watch Everton if I can. My wife and I have two daughters, one of them is aged 3 and the other was born in March this year.

Calendar


MATH20912: Example Sheet 5

American Put Option, Replicating Portfolio and Arbitrage: Examples to accompany lecture 11.

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MATH60082: The Finite Difference Method

We introduce the concept of finite differences, and how they can be used to solve parabolic equations.

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MATH60082: Examples Sheet 5

Step by step guide to binomial pricing. Some examples of the effect of discontinuous payoff on a numerical calculation, with some possible solutions.

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MATH60082: Solutions Sheet 5

Step by step solutions for Examples Sheet 5.

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MATH20912: Solutions Sheet 4

Solution to examples sheet 4.

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MATH20912: Example Midterm Test

Practice test for 9th March. We will go through this in week 6 examples classes.

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Research: Optimal costless extraction rate changes from a non-renewable resource

Evatt, G. W., P. V. Johnson, P. W. Duck and S. D. Howell, "Optimal costless extraction rate changes from a non-renewable resource", 2014, European Journal of Applied Mathematics

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Research: SLADI---a semi-Lagrangian alternating-direction implicit method for the numerical solution of advection-diffusion problems with application to electricity storage

Hernandez Avalo, J., P. V. Johnson and P. W. Duck, "SLADI---a semi-Lagrangian alternating-direction implicit method for the numerical solution of advection-diffusion problems with application to electricity storage", forthcoming 2015, Journal of Computational Finance

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