Annual meeting on STOCHASTIC PROCESSES STOCHASTIC CALCULUS AND APPLICATIONS Rome September 19-20, 2002

The conference will take place at the Department of Mathematics “G.Castelnuovo”, Università di Roma La Sapienza, and is supported by the MURST2001 funds for the COFIN project “Processi Stocastici, Calcolo Stocastico e Applicazioni”, universities of Rome-La Sapienza and Rome-Tor Vergata local units.

The conference will include invited talks and short talks on

· finance

· risk modelling

· filtering and control theory

· simulation

The following invited speakers will participate:

Paul Glasserman, Columbia University, New York

“Importance Sampling in Finance” (abstract)

Claudia Klueppelberg, University of Muenchen

“Extreme behaviour of stochastic processes

with applications to risk management” (abstract and slides of the talk)

Thomas G. Kurtz, University of Wisconsin, Madison

“Stochastic equations

for spatial birth and death processes” (abstract and slides of the talk)

Laurent Massoulié, Microsoft, Cambridge

“Epidemic-style information dissemination” (abstract)

Programme, abstracts and list of participants are available online.

No registration fee is requested but, please, register your participation by sending an e-mail including name, affiliation and e-mail address to processi@mat.uniroma2.it

People are warmly invited to present short talks. Please, send an abstract (in TeX or LaTeX or text format preferably-anyway no Word files) before September 10 (please!) to processi@mat.uniroma2.it

For information about hotels in Rome, see the website http://www.venere.com/it/roma/index.html.en (in particular, click on Università, Marsala (staz. Termini), San Lorenzo).

For futher information, contact:

Giovanna Nappo (nappo@mat.uniroma1.it) or Lucia Caramellino (caramell@mat.uniroma2.it).

The scientific committee,

P. Baldi, L. Caramellino, G. Nappo, M. Piccioni, F. Spizzichino

Paul Glasserman

Columbia University, New York

“Importance Sampling in Finance”

Monte Carlo simulation is widely used in finance for the pricing of derivative securities and for risk management. Importance sampling is a technique for reducing the variance of simulation estimates through a change of measure that increases the probability of "important" outcomes. This talk discusses the application of importance sampling to finance. One application changes the drift of an underlying Brownian motion in the pricing of path-dependent options; the drift is selected through an optimization problem that depends on the form of the option payoff. A second application increases the probability of large changes in market prices to estimate the tail of a portfolio loss distribution. We discuss various notions of asymptotic optimality for importance sampling estimators and distinguish light-tailed and heavy-tailed settings.

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Claudia Klueppelberg

University of Muenchen

“Extreme behaviour of stochastic processes

with applications to risk management”

Extreme value theory has been taylored for the mathematical/probabilistic modelling of rare events. Meanwhile it has become an important tool in quantitative risk management. For univariate iid data it is a standard application of this theory to estimate downside risk measures as the Value-at-Risk, which are based on a very low quantile. It is well-known, however, that financial data often show a dependence structure which can be modelled by diffusion models or (G)ARCH

models. Such models capture heavy-tailedness and clustering in the extremes which affects the quantile estimation. We describe the extremal behaviour of such volatility models.

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Thomas G. Kurtz

University of Wisconsin, Madison

“Stochastic equations for spatial birth and death processes”

Spatial birth and death processes of the type to be considered were first studied systematically by Preston in the 1970s. They began to play a central role in spatial statistics a few years later when Ripley recognized that important classes of spatial point processes (Gibbs distributions) could be obtained as stationary distributions of birth and death processes and that this characterization provided a computationally feasible method of simulation of the spatial point process (Markov chain Monte Carlo). In the mathematical arena, the infinite population versions provide a class of nonlattice interacting particle systems. Stochastic equations driven by Poisson random measures will be formulated for a large class of birth and death processes. The relationship to the corresponding martingale problem will be discussed. Conditions for existence and uniqueness and ergodicity (spatial and temporal) in the infinite population setting will be given. Application of Baddeley's time invariance estimation methods will be illustrated.

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Laurent Massoulié

Microsoft, Cambridge

“Epidemic-style information dissemination”

This talk is concerned with epidemic-style, or gossip-based information dissemination, according to which each participant of a group propagates information by "gossiping" to, or "infecting", a few random selected group members. In a first part of the talk we show how classical results on epidemic spread, and on the connectivity of random graphs, can characterise the performance of such information dissemination techniques. In particular we investigate the robustness of the Erdos-Renyi law for the connectivity of random graphs. In a second part, we consider the problem of designing "good" random graphs for information dissemination. This leads us to consider models of graph growth, and graph rebalancing.

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