Dr Kees van Schaik

Senior Lecturer in Actuarial Science (part of the Probability and Statistics Group)
Programme Director MSc Actuarial Science

Office 2.142
Department of Mathematics
Alan Turing Building
University of Manchester
Oxford Road, Manchester M13 9PL, UK
Email:
Phone: +44 (0)161 2755853

Office hour:

Papers:

My recent papers are available on ArXiv. A collection of papers produced by members of the Probability and Statistics Group can be found here.

• Optimal stopping of the stable process with state-dependent killing (with Alex Watson and Xin Xu), Bernoulli, vol. 31(1), 609-629 (2025). arXiv:2207.03610.
• Optimal switching between two spectrally negative Lévy processes to minimise ruin probability (with Ronnie Loeffen and José Eduardo Martínez Sosa), submitted.
• Optimally stopping at a given distance from the ultimate supremum of a spectrally negative Lévy process (with Monica Carvajal Pinto), Advances in Applied Probability, vol. 53(1), 279--299 (2021). arXiv:1904.11911.
• Applying the Wiener-Hopf Monte Carlo simulation technique for Lévy processes to path functionals such as first passage times, undershoots and overshoots (with Albert Ferreiro-Castilla), Journal of Applied Probability, vol. 52(1), 129--148 (2015). arXiv:1306.3923.
• A variation of the Canadisation algorithm for the pricing of American options driven by Lévy processes (with Florian Kleinert), Stochastic Processes and their Applications, vol. 125(8), 3234--3254 (2015). arXiv:1304.4534.
• Predicting the time at which a Lévy process attains its ultimate supremum (with Erik Baurdoux), Acta Applicandae Mathematicae, vol. 134, 21--44 (2014). arXiv:1207.4736.
• On the density of exponential functionals of Lévy processes (with Juan Carlos Pardo and Victor Rivero), Bernoulli, vol. 19(5A), 1938--1964 (2013). arXiv:1107.3760.
• Asymptotic distributions of the overshoot and undershoots for the Lévy insurance risk process in the Cramér and convolution equivalent cases (with Philip Griffin and Ross Maller), Insurance Mathematics and Economics, vol. 51, 382--392 (2012). arXiv:1106.3292.
• A Wiener-Hopf Monte Carlo simulation technique for Lévy processes (note: revised version) (with Alexey Kuznetsov, Andreas Kyprianou and Juan Carlos Pardo), Annals of Applied Probability, vol. 21, 2171--2190 (2011) arXiv:0912.4743.
• Further calculations for the McKean stochastic game for a spectrally negative Lévy process: from a point to an interval (with Erik Baurdoux), Journal of Applied Probability, vol. 48, 200--216 (2011). arXiv:0910.4621v1.
  (the SAGE code for this paper can be found here.)
• Perpetual convertible bonds with credit risk (with Christoph Kühn), Stochastics, vol. 80, 585--610 (2008).
• Pricing Israeli options: a pathwise approach (with Andreas Kyprianou and Christoph Kühn), Stochastics, vol. 79, 117--137 (2007).
• Finite expiry Russian options (with Andreas Kyprianou and Hans Duistermaat), Stochastic Processes and their Applications, vol. 115, 609--638 (2005).

Some slides of talks:

• A Wiener-Hopf Monte Carlo simulation technique for Lévy processes (Crossing Barriers: hitting and stopping time problems in finance and insurance, 2010, Bath)
• On the McKean game driven by a spectrally negative Lévy process (Optimal Stopping with Applications, 2009, Turku, Finland)

Stuff:

• An experimental interactive plotter (best viewed in a non-IE browser)
  It plots the solution to the McKean stochastic game driven by a jump-diffusion with negative directed, exponential jumps. Parameters of the process and the payoff functions can be chosen.
  It uses no other techniques than the plain old HTML and Javascript, thanks to the promising new <canvas>-element from the HTML5-specifications. Known problems:
  * IE: the explorercanvas project is used since IE has no native support for the <canvas>-element (yet).
  * IE: it seems that IE/explorercanvas goes wrong somewhere if the left end point on the x-axis is not chosen strictly positive
  * IE: labels at the axisses don't (always) show up at the right position, is an issue with explorercanvas apparently
  * Too exotic parameter values can yield overflows in the internal calculations, resulting in errors like "The internal variable <...> has the value Infinity, while it should be numeric."
• PyBib. If you, like me, keep all your references in one (large) .bib file and find producing an inline bibliography one of the most annoying things when preparing a paper this little (GUI-)tool might be useful. It takes a .bib file and a .tex file, goes through the .tex file looking for references (i.e. \cite{...} commands), links each of these references with the right entry in your .bib file and uses the information in the .bib file to build an inline bibliography. All you need to do is copy the output and paste it into your .tex file. :).
  It requires Python 2.x with x>=4. If you're on Linux this is (usually) available by default. After downloading, use "chmod +x PyBib.py" to make the file executable and run it. If you're on Windows you might have to install Python from the Python website (you can test whether Python is already installed by trying to run the command "python" in a command box). When you have Python available and downloaded the script, run the command "pyhtonw PyBib" to launch the program.

Some places I have studied/worked/visited:

• Utrecht University, Utrecht, Netherlands
• Frankfurt University, Frankfurt, Germany
• REAAL insurances (Dutch), Utrecht, Netherlands
• Bath University, Bath, UK
• CIMAT, Guanajuato, Mexico
• ANU, Canberra, Australia

A few random links:

• The beauty of Bath
• An American's view on biking in Amsterdam
• The Truth About Amsterdam (a response to an item on the 'fair and balanced' FOX news)
• dEUS. Without any doubt probably one of the best bands in the world
• Videos of talks from the International Congress of Mathematicians. From 1998 on, incl. e.g. Wiles on Fermat's problem
• Mathematica is a brilliant product. However it costs a lot of money. And it is, despite the documentation, a black box. Relying on it means seriously jeopardising the very basic building blocks of modern science: reproducibility and verifiability. Because we can't be sure what algorithm is actually being used to solve what problem, and we can't verify any of the steps in a result/proof. Luckily there's SAGE.