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STOCHASTIC
METHODS IN MATHEMATICAL FINANCE
Rome
September 15-17, 2005
Dedicated to
Bruno Bassan |
The
conference will take place at the Department of
Mathematics G.Castelnuovo,
Universitą di Roma La Sapienza,
and is supported by the MIUR2004 funds for the COFIN/PRIN project Metodi
stocastici in finanza matematica.
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·
Claudia Ceci, Universitą
di Chieti ·
Isaco Meilijson,
University of Tel Aviv ·
Yoseph Rinott,
University of Jerusalem ·
Marco Scarsini, Universitą
di Torino ·
Carlo Sempi, Universitą di Lecce: Semicopulę and
their transforms [abstract] |
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September 16-17. The
conference will include invited talks and short talks on finance, risk
modelling, filtering and control theory, simulation.
The following invited speakers have confirmed
their participation:
·
Ruediger Frey,
University of Leipzig
·
Frederic Patras, CNRS Nice and Zeliade systems: Correlation in the credit risk market:
current trends and problems [abstract]
·
Maurizio Pratelli, Universitą
di Pisa: Merton's Mutual Fund Theorem:
the classical version and some generalizations in infinite dimensional financial
models [abstract]
No registration fee is requested but, please,
register your participation by sending an e-mail including name, affiliation and
e-mail address to mestofin@mat.uniroma1.it
The following information are available:
PARTICIPANTS (registered up
to September 12)
Some
additional information:
how to reach the Campus of the University of Rome
“La Sapienza”
the position of the Department
of Mathematics inside the Campus
For further information, please contact the
organizers at mestofin@mat.uniroma1.it
The scientific committee:
Wolfgang Runggaldier (Padova), Paolo Baldi (Roma-Tor
Vergata), Lucia Caramellino (Roma-Tor Vergata),
Giovanna Nappo (Roma-La Sapienza), Fabio Spizzichino (Roma-La Sapienza)
The
local organizing committee
Lucia
Caramellino (Roma-Tor Vergata), Claudia Ceci (Pescara), Claudio Macci (Roma-Tor
Vergata), Giovanna Nappo (Roma-La Sapienza), Fabio Spizzichino
(Roma-La Sapienza), Gianluca Torrisi (IAC-CNR, Roma)
Optimal stopping and mixed problems with semicontinuous reward:
regularity of the value function
and viscosity solutions
Claudia Ceci
Universitą di Chieti
References
1. B.Bassan-C.Ceci: An optimal stopping problem
arising from a decision model with many agents. Probab. Engrg. Inform. Sci., 12,
pp.1-16, 1998.
2. B.Bassan-C.Ceci: Optimal stopping with
discontinuous reward: regularity of the value function and viscosity solution. Stochastics Stochastics Rep., 72, 55-77, 2002.
3. B.Bassan-C.Ceci: Regularity of the value
function and viscosity solutions in optimal stopping problems for general
Markov processes. Stochastics Stochastics
Rep., 74, 633-649, 2002.
4. C.Ceci-B.Bassan: Viscosity approach for
mixed control problems: semicontinuity of the stopping reward. Stochastics Stochastics Rep., 76, 323-337, 2004.
Some stochastic orders related to
portfolio diversification and to selective risk aversion
Isaco
Meilijson
University of
Tel Aviv
Abstract. Rothschild &
Stiglitz (1971) showed that if Y is more dispersed than X in the
second-degree (or Martingale dilation) sense, then although
(i) the best portfolio between X and some
constant interest rate is preferred by any risk averter to the best
portfolio between Y and the same constant,
it may well happen that
(ii) the optimal fraction invested on Y may
exceed the optimal fraction invested in X.
That is, the demand for the safer asset may be
lower.
This talk will review some stronger stochastic
orders (Gollier, Landsberger, M., others) that better determine demand.
Some of these stochastic orders have applications to "selective risk
aversion", as modelled by "star-shaped utilities", and to
some interesting martingale material by Azema and by Yor.
This subject, to be surveyed, was one of
the my many joint interests with Bruno Bassan.
Inference on multi-phase survival processes
with incomplete data
Yoseph
Rinott
University of
Jerusalem
Abstract.
Consider
a life consisting of several phases (e.g., a disease which progresses in
phases) and data obtained by intercepting the life process at a random
time and following it for a limited time. The data is therefore biased
and censored. We obtain information on the phase at which a subject is
intercepted, and perhaps on the past of the process. Using models (e.g.,
copulas) we wish to infer on the distribution of total life, and the joint
distribution of the phases' durations.
Based on joint works with Bruno Bassan, Micha
Mandel, Yehuda Vardi and Cun-Hui Zhang.
Stochastic
orders and lattices of probability measures
Marco Scarsini
Universitą di Torino
Abstract. We study various partially
ordered spaces of probability measures and we determine which of them are
lattices. This has important consequences for optimization problems with
stochastic dominance constraints. In particular, we show that the space of
probability measures on R is lattice
under most of the known partial orders, whereas the space of probability
measures on Rd typically is
not. Nevertheless, some subsets of this space, defined by imposing strong
conditions on the dependence structure of the measures, are lattices.
Semicopulę and their transforms
Carlo Sempi
Universitą di Lecce
Abstract.
The
concept of semicopula was introduced in the statistical literature by Bruno
Bassan and Fabio Spizzichino. It generalizes the notions of quasi--copula and,
hence of that of copula. Moreover, it is also related to the notion of
triangular norm. Here we present the main properties of semicopulas, give
several examples, show that they form a compact subset of the set of all
functions from $[0,1]^2$ into $[0,1]$. and that they are a complete lattice
when the natural pointwise order is considered. For the applications it is
important to study the transformation
C_h (x,y) :=
h^{[-1]} C( h(x) , h(y) ),
where $C$ may be a semicopula, a quasi--copula
or a copula.
This talk is a joint work with Fabrizio
Durante.
Pricing portfolio credit derivatives in a Markovian model of default
interaction
Ruediger
Frey
University of
Leipzig
Abstract. The market for
portfolio credit derivatives has seen rapid growth in recent years. and dynamic
models for portfolio credit risk have become indispensable tools for the
pricing of these products. We discuss models with default contagion,
i.e. models where the default of a firm has an impact on the default
intensity of other firms in a portfolio. Particular emphasis will be given
to the pricing of portfolio credit derivatives such as CDOs in Markovian
model for default contagion, which is an alternative to the copula models
popular in industry.
Background information can be found in the
forthcoming book "Quantitative Risk Management, Concepts, Techniques and
Tools" by A. McNeil, R. Frey and P. Embrechts (Princeton University
Press 2005).
Correlation in the credit risk market: current
trends and problems
Frederic Patras
CNRS Nice and
Zeliade systems
Abstract. Due to the fast
development of CDOs, n-to-default swaps and other so-called correlation
products, the understanding and modelling of correlation, and particularly of
defaults correlation, has become one of the leading problems for credit
practitioners. The talk will concentrate mainly on CDOs and survey, besides the
historical development of the financial products and models, some recent ideas
in the field, such as stochastic correlation, the definition of local
correlation or the dynamic modelling of defaults.
Merton's Mutual Fund Theorem: the classical
version and some generalizations in infinite dimensional financial models
Maurizio Pratelli
Universitą di Pisa
Abstract. The original proof of the
celebrated "Merton's mutual fund theorem" is based on stochastic
control methods (solution of an Hamiton-Jacobi-Bellman equation): in this talk,
I will show how an easy proof of this theorem can be given with "stochastic
calculus" methods (representation of martingales in a Brownian
filtration). This method can be applied to infinite dimensional situations: the
so called "large financial markets" (where a sequence o assets is
taken into account) and "bond markets" (where there is a continuum of
assets). The talk will insist on related infinite-dimensional stochastic
integration problems.