Maxwell Institute Probability Day, December 2014


Monday 8 December 2014

Venue and session details

Heriot-Watt University, Edinburgh. For details of how to get to Heriot-Watt University, click here.

Lunch will be provided. Meet at 12.15 outside room S.01 of the Colin Maclaurin Building (building 22 on this campus map).

Talks from 12.55 - 15.00 will be held in room S.01 and chaired by Sergey Foss.

Tea and coffee will be served from 15.00 - 15.30 in the common room (F.01) of the Colin Maclaurin building.

Talks from 15.30 - 17.35 will be held in room T.01 of the Colin Maclaurin Building, and will be broadcast as part of the SMSTC Probability Stream. This session will be chaired by Istvan Gyongy.



12.15 - 12.55:Lunch (provided). Meet outside room S.01.
12.55 - 13.00:Opening (Sergey Foss)
13.00 - 13.40:Gonçalo dos Reis
Securitization and equilibrium pricing under relative performance concerns
We investigate the effects of a finite set of agents interacting socially in an equilibrium pricing mechanism. A derivative written on non-tradable underlyings is introduced to the market and priced in an equilibrium framework by agents who assess risk using convex dynamic risk measures expressed by Backward Stochastic Differential Equations (BSDE). An agent is not only exposed to financial and non-financial risk factors, but he also faces performance concerns with respect to the other agents. The equilibrium analysis leads to systems of fully coupled multi-dimensional quadratic BSDEs. Within our proposed models we prove the existence and uniqueness of an equilibrium. We show that aggregation of risk measures is possible and that a representative agent exists. We analyze the impact of the problem's parameters in the pricing mechanism, in particular how the agent's concern rates affect prices and risk perception.
13.40 - 14.20:Michela Ottobre
Smoothing and long time behaviour of hypocoercive-type Markov semigroups
We present a completely analytic method, alternative to Malliavin calculus, to study smoothing properties and long time behaviour of (the derivatives, of any order of) degenerate Markov semigroups. We will consider in particular the case in which the generator of the semigroup is a differential operator of hypoelliptic/hypocoercive type. This kind of operators are of interest in non-equilibrium statistical mechanics, in the context of the heat bath formalism. As an application/motivation for introducing this new technique we will look at systems of infinitely many interacting diffusions. The method we introduce is a combination of the classic Bakry-Emery approach together with the hypocoercivity theory recently introduced by C. Villani.
14.20 - 15.00:Laila El Ghandour
The valuation of storage technologies in the UK's power market
As a greater proportion of the UK's power generation capacity is provided by wind power, the problem of balancing supply and demand on the grid becomes stochastic and the ability to store power becomes more valuable. We develop a model to asses the impact of different power storage technologies, such as pumped storage, CAES and batteries, on the UK power system. We employ recently developed tools in stochastic optimal control to assess if a storage technology is economically viable.
15.00 - 15.30:Break (tea and coffee provided in the common room)
15.30 - 16.10:Fraser Daly
Geometric-type approximations for distributions with monotone failure rate
We will examine how assumptions of a monotone failure rate can help in proving explicit error bounds in approximation by geometric and compound geometric random variables. Applications will be given to the M/G/1 queue and Poisson processes. The proofs employ Stein's method for probability approximation.
16.10 - 16.50:David Siska
Convergence of tamed Euler schemes for a class of stochastic evolution equations
We prove stability and convergence of a full discretization for a class of stochastic evolution equations with super-linearly growing operators appearing in the drift term. This is done by using the recently developed tamed Euler method, which employs a fully explicit time stepping, coupled with a Galerkin scheme for the spatial discretization.
16.50 - 17.30:Xiling Zhang
Almost Sure And V-Stability of Tamed Euler Schemes
Strong convergence of various taming technique for SDE approximation with nonlinear coefficients has been developed recently, but yet some other properties, such as stability, have hardly been investigated. When the equilibrium of a SDE is (almost surely or L^P) stable, the numerical solution can fail to preserve the corresponding property. In this talk I will introduce a sufficient condition to recover the stability of tamed Euler schemes. Also I will give specific requirements for each example of different tamed schemes.
17.30 - 17.35:Closing (Istvan Gyongy)


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


The organisers gratefully acknowledge financial support from the Maxwell Institute.