Download Financial Mathematics and Applied Probability Seminars 2006-2007

Financial Mathematics and Applied Probability Seminars 2006-2007
Unless otherwise indicated, all seminars take place at Lecture Theatre 2C, King's College
London, The Strand, London WC2R 2LS.
Tuesday 24 Dr Reimer Kuehn
October, Department of Mathematics, King's College London
5:30 pm
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 Professor Ralf Korn
October, Department of Mathematics, University of Kaiserslautern
5:30 pm
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, risk-averse 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 Dr Martijn Pistorius
November, Department of Mathematics, King's College London
5:30 pm
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 bail-out 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 Dr David Hobson
November, Department of Mathematics, University of Bath
5:30 pm
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 Professor Goran Peskir
November, Department of Mathematics, University of Manchester
5:30 pm
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, free-boundary problem, local time-space
calculus, smooth fit, curved boundary.
Tuesday 5 Professor William Shaw
December, Department of Mathematics, King's College London
5:30 pm
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 Dr Pavel Gapeev
January, Weierstrass Institute for Applied Analysis and Stochastics, Berlin
5:30 pm
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
jump-diffusions, which are needed for the parameter calibration of the model.
Monday 29 Professor Tomas Bjork
January, Stockholm School of Economics
5:30 pm
Optimal investment under partial information
Room 1B27
Tuesday 6 Dr Aleksandar Mijatovic
February, Institute for Mathematical Sciences, Imperial College London
5:30 pm
Spectral methods for volatility derivatives
Tuesday 6 Professor Nick Bingham
March,
Department of Probability and Statistics, University of Sheffield
5:30 pm
Tuesday 13 Professor Mark Davis
March,
Department of Mathematics, Imperial College London
5:30 pm
Outperforming a benchmark via risk-sensitive control
This paper extends the risk-sensitive 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 Levy-driven price models will be considered.
Joint work with Sebastien Lleo.
Tuesday 20 Dr Alvaro Cartea
March,
Commodities Finance Centre, Birkbeck, London
5:30 pm
Tuesday 29 Dr Dirk Becherer
May,
Department of Mathematics, Imperial College London
5:30 pm
Tuesday 16 Dr Umut Cetin
October, Department of Statistics, London School of Economics
5:30 pm