Maxwell Institute Probability Day, April 2015


Monday 20 April 2015


James Clerk Maxwell Building, King's Buildings, University of Edinburgh. For details of how to get to King's Buildings, click here.

Lunch will be provided. Meet at 12.00pm in the common room (Room 5213a on the fifth floor) of the JCMB.

Talks will be held in Room 6301 of the JCMB.



12.00 - 13.00:Lunch (provided: Room 5213a, JCMB)
13.00 - 13.05:Opening
13.05 - 13.40:Marcus Christiansen
Dynamics of solvency risk in life insurance liabilities
Modern solvency risk management is a continuous effort based on monitoring of risks and reacting timely when necessary. This motivates to take a dynamic perspective within a time-continuous framework. We describe the time dynamics of the solvency level of life insurance contracts by representing the solvency level and the underlying risk sources as the solution of a stochastic forward-backward system. This leads to an additive decomposition of the total solvency level with respect to time and different risk sources. The decomposition turns out to be an intuitive tool to study risk sensitivities. We study two methods to obtain explicit representations: via linear partial differential equations and via a Monte Carlo method based on Malliavin calculus. The forward-backward system provides the groundwork for stochastic control with solvency level objectives. We will give an outlook on interesting yet unsolved control problems.
13.40 - 14.15:Peter Richtárik
Randomized primal and dual optimization methods with arbitrary sampling
State-of-the-art scalable optimization algorithms for certain applications (e.g., machine learning) often rely on the idea of randomized decomposition. For instance, if the function to be minimized arises as the sample average approximation in a prediction task, it will have the form of the average of a very large number of loss functions. In such a case one may wish to randomly sample a data point, corresponding to a single loss function, and use that information to construct an iteration. Alternatively, one may want to sample a subset of these data points (a minibatch), and construct a search direction based on this more informative sample. Methods based on the idea of stochastic gradient descent (stochastic approximation) are very widely used in practice. The dual formulation of such problems involve the minimization of a function in a very large dimensional space. In order to tackle such problems, one may wish to in each iteration only move in a random subspace formed as the span of a random subset of coordinates which correspond to a mini batch of data points. Popular methods for such problems include randomized coordinate descent.

In this talk I will describe a unified theory of randomized decomposition methods in the primal and dual spaces with complexity guarantees vastly superior to classical algorithms. The theory is developed for an arbitrary minibatching scheme: an arbitrary random set-valued mapping governing the choice of data points which inform the progress in each iteration. The resulting complexity bounds are compact and simple to understand, and shed light on the role of randomization in the development of modern optimization algorithm for tackling big data problems.

14.15 - 15.00:Break (tea and coffee provided: Room 5213a, JCMB)
15.00 - 15.35:Máté Gerencsér
A weak Harnack inequality for SPDEs
We consider stochastic parabolic partial differential equations under minimal assumptions: the coefficients are merely bounded and measurable and satisfy the stochastic parabolicity condition. Adapting De Giorgi's iteration technique to the stochastic setting, boundedness of the solutions is established, moreover, a weak Harnack inequality is derived. In the deterministic case, such a Harnack inequality immediately implies Hölder continuity of the solutions. This step is more elusive in the stochastic case, but a weaker type of continuity can be obtained.
15.35 - 16.10:Damian Clancy
Approximating persistence time in infection models
I will review various methods that have been proposed to approximate the expected time to disease extinction in simple stochastic infection models.
16.10 - 16.15:Closing


Attendance at the talks is free and there is no need to register. If you have any questions, please contact either Gonçalo dos Reis or Fraser Daly.


The organisers gratefully acknowledge financial support from the Maxwell Institute.