CMCM Distinguished Visitor Lectures, Jyväskylä Fri 19 May
Pekka Orponen
Department of Mathematics
Department of Statistics
The following CMCM Distinguished Visitor Lectures will
be presented on Friday, 19 May:
Prof. D. M. Titterington (Glasgow),
"Aspects of Inference for Mixture Distributions and
Related Problems"
Prof. B. Øksendal (Oslo and Bergen),
"Optimal consumption and portfolio in a market with
partial observation"
The lectures take place in Room MaD380 on the Mattilanniemi
campus of the University of Jyväskylä at 11-13 (Titterington)
and 14:00(!)-16 (Øksendal). Abstracts are enclosed.
Welcome!
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ASPECTS OF INFERENCE FOR MIXTURE DISTRIBUTIONS AND
RELATED PROBLEMS
D. M. Titterington, University of Glasgow
The talk will present a wide review of recent research on
mixture distributions and generalisations thereof. After
the underlying framework has been established, recent
progress on some of the most important current issues will
be outlined, in both frequentist and Bayesian inference.
For example, various recent approaches will be described to
the question of assessing how many components are present in
an underlying mixture distribution. Mention will also be made
of generalisations of the mixture model, including hidden
Markov chains, hidden Markov random fields and the hierarchical
mixtures of experts model; the extent to which inference becomes
more complicated with these models will be discussed.
This will lead on to a discussion of a body of material in the
neural-computing literature, where mixture-type models and their
analysis have attracted recent attention and some new ideas have
been created.
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OPTIMAL CONSUMPTION AND PORTFOLIO IN A MARKET WITH
PARTIAL OBSERVATION
Bernt Øksendal,
University of Oslo and Norwegian School of Economics and Business
Administration, Bergen
Usually the mathematical models in finance assume that the agents
have complete information about the parameters involved. For example,
in the classical Black - Scholes model the stock price is modelled by
a geometric Brownian motion X(t) of the form
dX(t) = \mu X(t) dt + \sigma X(t) dB(t) ( B(t) being Brownian motion),
where one assumes \mu and \sigma are known constants.
In reality however, these constants are not known, but have to be
estimated based on observations of the stock price X(t). If this is
taken into account, we get a mathematical model with partial
observation.
In this talk we give a short survey of some known results for such
partial observation finance models in complete markets. In the end
we also mention some recent results in the incomplete market case.
The talk is partially based on joint work in progress with
Agnès Sulem, INRIA.