Dr Kees van Schaik

Senior Lecturer in Actuarial Science (part of the Probability, financial mathematics and actuarial science "theme") Department of Mathematics, University of Manchester

• Address: Office 2.142, Alan Turing Building, Oxford Road, Manchester M13 9PL, UK
• Email:
• I'm not AI (yet, at least): bland UoM personel page

Online course materials:

• MATH4/67201 Martingale Theory
• MATH37542 Tools for Risk Management

Research papers:

My recent papers are available on ArXiv. A collection of papers produced by colleagues in the whole Dept of Maths 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)

Some places I have studied/worked/visited:

• Utrecht University, Utrecht, Netherlands ("doctoraal wiskunde", similar to MMath in the UK)
• Frankfurt University, Frankfurt, Germany (PhD in Probability/Financial Maths under Prof Christoph Kühn)
• REAAL insurances (Dutch), Utrecht, Netherlands (actual proper job as "actuarial researcher"...)
• Bath University, Bath, UK (eek, quickly back to academia for a postdoc under Prof Andreas Kyprianou!)
• CIMAT, Guanajuato, Mexico (extended research visit)
• ANU, Canberra, Australia (another postdoc, under Prof Ross Maller)

A few random links:

• The beauty of Bath
• An American's view on cycling 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.