Financial Mathematics and Applied
Probability Seminars 20062007
Unless otherwise indicated, all seminars take place at Lecture Theatre 2C,
King's College London, The Strand, London WC2R 2LS.
Tuesday 24 October, 5:30 pm 
Dr Reimer Kuehn
Department of Mathematics, King's College London
Credit Contagion and Credit Risk
Abstract:
We look at the influence of economic interactions on credit risk.
Starting point
is the observation that a default of a company has material effects
on the economic
well being of other companies engaged in direct economic interactions
with it, and
that this effect induces dynamically induced functional correlations
rates rather
than mere statistical correlations of default rates in a network of
interacting
firms. We introduce and solve a model describing the default
dynamics within a
heterogeneous network of interacting firms. For large average
connectivities within
the network, the dynamics can be solved in closed form, and
distributions of default
rates and loss distributions can be computed. While effects of
economic interactions
are weak in typical (most probable) scenarios, they are pronounced in
situations of
economic stress, and lead to a significant fattening of tails of loss
distributions
in large loan portfolios. Interestingly, the collective behaviour of the
system is
described by very few parameters describing the low order statistics of
the parameters characterising the economy.

Tuesday 31 October, 5:30 pm

Professor Ralf Korn
Department of Mathematics, University of Kaiserslautern
Inflation: modelling, hedging and optimization
Abstract:
We consider the optimal investment problem for an investor who can
choose between a
riskless money market account, risky stocks and inflation linked
products. Modelling the
evolution of an inflation index is motivated by macroeconomic reasoning
such as the
Fisher equation and is based on Korn and Kruse (2004). As a main result,
riskaverse
investors will typically not invest in the inflation products considered
by us, but they will
be used by (institutional) investors that have to hedge inflation risk.

Tuesday 14 November, 5:30 pm 
Dr Martijn Pistorius
Department of Mathematics, King's College London
On the optimal dividend problem
Abstract: In this talk we consider the problem of determining
optimal dividend distribution policies for an insurance company.
Modelling the risk process of the insurance company before
dividends are deducted by a spectrally negative Levy process,
the classical dividend problem is to find a dividend payment
policy that maximizes the total expected discounted dividends.
Related is the problem where
we impose the restriction that ruin be prevented: the
beneficiaries of the dividends must then keep the insurance
company solvent by bailout loans. Drawing on the fluctuation
theory of spectrally negative Levy processes we give an
explicit analytical description of the optimal strategy in the set of
barrier strategies and the corresponding value function,
for either of the problems. Subsequently we investigate when the
dividend policy that is optimal amongst all admissible ones
takes the form of a barrier strategy. (Joint work with
Florin Avram and Zbigniew Palmowski.)

Tuesday 21 November, 5:30 pm 
Dr David Hobson
Department of Mathematics, University of Bath
Skorokhod embeddings and finance
Abstract:
The standard approach in Mathematical Finance is to postulate a model, and
to use this model to derive the prices of financial derivatives.
There is often a middle step of calibrating a parametric family of models
against the prices of vanilla securities.
This talk will consider an alternative approach in which we do not
specify any model. Instead we consider the set of all possible price
proceses which are consistent with the traded prices of vanilla
securities. If the vanilla securities are calls then the problem of
identifying potential price processes can be identified with the Skorokhod
embedding problem with extremality properties.

Tuesday 28 November,
5:30 pm

Professor Goran Peskir
Department of Mathematics,
University of Manchester
Predicting the ultimate supremum of a stable Levy process
Key words and phrases: Stable Levy process (with no negative jumps),
optimal prediction, optimal stopping, ultimate supremum, fractional
Laplacian, RiemannLiouville fractional derivative, Caputo fractional
derivative, Volterra integral equations of the first and second kind,
freeboundary problem, local timespace calculus, smooth fit, curved
boundary.

Tuesday 5 December,
5:30 pm

Professor William Shaw
Department of Mathematics, King's College London
Copulas vs Canonical Multivariate Distributions: A multitude of T copulas and some Canonical Systems
Abstract:
The Normal Distribution and the Cauchy distribution sit at two extremes in terms of their tail structure and the existence of moments  how would one construct a bivariate distribution with each as a marginal but with dependency? How many Student T copulas are there and what are the implications of a choice and its relationship to classical distribution theory? This talk will present a reconciliation of current copula simulation theory with classical distribution theory for the case of the multivariate Student distribution, and will exhibit some new explicit bivariate distributions, together with practical simulation techniques for applied mathematical finance for the multivariate case. We will also see some new arguably "Canonical" distributions and new correlation formulae to assist with calibration. One outcome of our considerations is to present an alternative to the elliptical structures, currently popular in distribution theory and risk management, with the property that the marginals are truly independent in the zero correlation limit.

Tuesday 23 January,
5:30 pm

Dr Pavel Gapeev
Weierstrass Institute for Applied Analysis and Stochastics, Berlin
Constructing jump analogues of diffusions and application to finance
Abstract: We propose a method for construction of jump analogues of diffusion
processes solving stochastic differential equations driven by both a
Wiener process and a Poisson random measure, which admit explicit
solutions or are reducible to ordinary differential equations. We
illustrate the action of this method on some diffusions, which are
widely used in finance. We also give some remarks on calculation of the
Laplace transforms of the marginal distributions of the constructed
jumpdiffusions, which are needed for the parameter calibration of the
model.

Monday 29 January,
5:30 pm
Room 1B27

Professor Tomas Bjork
Stockholm School of Economics
Optimal investment under partial information

Tuesday 6 February, 5:30 pm 
Dr Aleksandar Mijatovic
Institute for Mathematical Sciences, Imperial College London
Spectral methods for volatility derivatives

Tuesday 6 March, 5:30 pm 
Professor Nick Bingham
Department of Probability and Statistics,
University of Sheffield

Tuesday 13 March, 5:30 pm 
Professor Mark Davis
Department of Mathematics, Imperial College London
Outperforming a benchmark via risksensitive control
This paper extends the risksensitive asset management theory developed
by Bielecki and Pliska and by Kuroda and Nagai to the case where the
investor's objective is to outperform an investment benchmark. The main
result is a mutual fund theorem. Every
investor following the same benchmark will take positions, in
proportions dependent on his/her risk sensitivity coefficient, in two
funds: the logoptimal portfolio and a second fund which adjusts for the
correlation between the traded assets, the benchmark and the underlying
valuation factors. Some extensions to Levydriven price models will be
considered.
Joint work with Sebastien Lleo.

Tuesday 20 March, 5:30 pm 
Dr Alvaro Cartea
Commodities Finance Centre, Birkbeck, London

Tuesday 29 May, 5:30 pm 
Dr Dirk Becherer
Department of Mathematics, Imperial College London



Tuesday 16 October, 5:30 pm 
Dr Umut Cetin
Department of Statistics, London School of Economics


