Seminar Programme 2011
Our seminars are open to the public and refreshments are provided. Seminar are given by leading academics as well as industry experts. Unless otherwise indicated, all seminars take place in Lecture Theatre K2.31, King's College London, The Strand, London WC2R 2LS.
Seminars normally last one hour and are followed by a question and answer session. Coffee and tea is served at 17:00 and the seminars themselves begin at 17:30.
Our next series of seminars will take place from January to March 2012.
If you are interested in joining our seminar mailing list, please contact Emily Balls (emily.balls@kcl.ac.uk).
Seminars in January - March 2012
Tuesday 17 January
Speaker: Professor William Shaw, University College London
Title: Risky Business
Abstract: Financial trades go wrong for many reasons beyond human deception and error, and the capacity for complex systems to display extreme behaviour is routinely underestimated. This lecture will explore the capacity of financial trades to go badly wrong, discuss how we talk about the associated risks and how the choice of terminology affects perception. The past failure of banks to set aside sufficient insurance will be discussed in mathematical terms, and some non-Gaussian models will be introduced from both a statistical basis and from a simple mathematical model of feedback and panic. These suggest more realistic capital allocations for insurance.
Tuesday 24 January
Speaker: Professor Nick Bingham, Imperial College London
Title: Multivariate prediction and matrix Szeg\”ö theory
Abstract: The theory of orthogonal polynomials on the unit circle (OPUC), originating with Szeg\"o, has recently been extensively developed, e.g. by Barry Simon and co-workers, and applied to prediction of stationary time series, e.g. in mathematical finance. The multivariatge theory (MOPUC) has recently been developed, e.g. by Sasha Pushnitski of KCL, and applied to prediction of stationary multivariate time series, e.g. in portfolio theory. The talk gives a survey of this rapidly expanding field.
Presentation
Tuesday 31 January
Speaker: Professor Dorje Brody, Brunel University
Title: Noise, risk premium, and bubble
Abstract: The existence of the pricing kernel is shown to imply the existence of an ambient information process that generates market filtration. This information process consists of a signal component concerning the value of the random variable X that can be interpreted as the timing of future cash demand, and an independent noise component. In the Brownian setup, the conditional expectation of the signal determines the market risk premium vector. An addition to the signal of any noise is shown to change the drifts of price processes in the physical measure, without affecting the current asset-price levels. Such a drift in the noise term can induce anomalous price dynamics, and can be seen to explain the mechanism of observed phenomena of equity premium and financial bubbles. (Based on joint work with Robyn Friedman and Grzegorz Andruszkiewicz.)
Tuesday 7 February
Speaker: Dr Ed Hoyle, Fulcrum Asset Management
Title: Liouville Processes, Archimedean Copulas and Realized Variance
Abstract: We describe the construction and properties of Liouville processes. A Liouville process is a multivariate, increasing, Markov process defined over a finite time horizon. The law of a Liouville process is equivalent to that of a multivariate gamma process. Archimedean survival processes (ASPs) form a subclass of the Liouville processes. ASPs have the remarkable property that the survival copula of their final value is an Archimedean copula. Furthermore, given any Archimedean copula $C$, there exists an ASP who's final value has survival copula $C$. We present an application of Liouville processes to the joint modelling of realized variance for two stock indices.
Tuesday 14 February
No seminar.
Tuesday 21 February
Speaker: Dr John Moriarty, University of Manchester
Title: Hysteretic regime switching diffusions, and applications in the theory of Real Options
Abstract: We will present some recent work at the interface between probability theory and Real Options Analysis. We show that certain industrial planning problems lead to the study of stochastic processes defined on time-varying graphs. We verify the uniqueness of solutions to the Feynman-Kac PDE for these processes, from which we obtain fast numerical solutions to data-driven industrial planning problems.
Tuesday 28 February
Speaker: Professor Steffen Dereich, University of Marburg
Title: Condensation effects in preferential attachment models with fitness
Abstract: A preferential attachment network model is a sequence of random graphs that is build according to a simple dynamic rule. In each step a new vertex is added and linked by a random or deterministic number of edges to the vertices already present in the system. In this process, links to vertices with high degree are preferred. A variant of the model, additionally, assigns each vertex a random positive fitness (say a~$\mu$-distributed value) which has a linear impact on its attractiveness in the network formation. Such network models show an intriguing phase transition.
In the condensation phase, a constant fraction of new links is attached to vertices with fitness getting closer and closer to the essential supremum of~$\mu$ although the proportion of such vertices decays to zero. This condensation effect was observed for the first time by Bianconi and Barab\'asi in 2001, where it was coined Bose-Einstein phase due to similarities to Bose-Einstein condensation. A first rigorous verification of the phenomenon was conducted by Borgs, Chayes, Daskalakis and Roch in 2007 for a particular variant of the model. How importance shifts to vertices with higher and higher fitness remained open. In this talk, I will present recent results on the dynamics of this process.
Tuesday 6 March
Speaker: Dr Miklos Rasonyi, University of Edinburgh
Title: Behavioural investors in multiperiod market models
Abstract: We consider the problem of optimal investment for an investor whose behaviour is described by cumulative prospect theory. Most of previous research focussed on one-period models. It turns out that the multiperiod case exhibits a number of new phenomena.
We provide easily verifiable conditions for the well-posedness of this problem and show the existence of optimal strategies in the case of power-like utilities and power-like distortion functions. We also have a look at what happens in continuous-time, in particular, we provide a sufficient and essentially necessary condition for the Black-Scholes model.
Tuesday 13 March
Speaker: Professor Ilya Pavlyukevich, University of Jena, Germany
Title: Dynamical systems perturbed by heavy-tailed Levy noise.
Abstract: We study the first exit times and metastable behaviour dynamical systems perturbed by small multiplicative Levy noise with heavy tails. A special attention is paid to the planar dynamical systems with stable limit cycles. As examples we consider Duffing and van der Pol oscillators in presence of stable Levy perturbation. (joint work with Michael Högele, U Potsdam)
Tuesday 20 March
Speaker: Professor Martin Schweizer, ETH Zurich
Title: Aspects of arbitrage old and new
Abstract: Having absence of arbitrage in some form has always been a desirable property for stochastic models of financial markets. On finite probability spaces or in finite and discrete time, it is clear how to give both a precise mathematical formulation for this economic property and an equivalent probabilistic description: "Absence of arbitrage is equivalent to the existence of an equivalent martingale measure for discounted asset prices."
In infinite-horizon models or in continuous time, things become more subtle. The famous NFLVR condition due to Delbaen-Schachermayer has the pleasant feature of again allowing one to prove a similar mathematical theorem, but it also has certain drawbacks. In this talk, we discuss some new directions in arbitrage theory and show some new results. One of those can be viewed as a continuous-time version of the classical Dalang-Morton-Willinger result, and rather remarkably, its proof requires separation theorems in an infinite-dimensional space.
The talk is based on joint work with Tahir Choulli (University of Alberta, Edmonton).
Tuesday 27 March
Speaker: Professor Michael Dempster, Centre for Financial Research, University of Cambridge
Title: Regulating complex derivatives: Can the opaque be made transparent?
Abstract: This paper discusses the general principles governing the relationships between banks issuing over-the-counter (OTC or bespoke) structured derivatives to non-bank clients. After a discussion of the evident informational asymmetries between the counterparties to such deals, a representative sample is presented of recent deals failed from the client’s viewpoint, all the subject of current negotiation or litigation with banks. Mathematical (mis)pricing and (asymmetric) counterparty risk assessments for these examples are summarized graphically before considering the legal implications of their egregious features. Possible mitigation of these features in future deals by appropriate regulation and interpretation in the world’s courts and the reputational and systemic consequences of regulation/litigation/default on the positive mark-to-market of their leading issuers are discussed. The talk is based on work with E A Medova & J Roberts (Centre for Financial Research, University of Cambridge & Ludwig Maximilians Universität, Munich).
Presentation