Seminar on
Stohastics
Seminar on
Stohastics
PROGRAM
Recently several authors have introduced classes of functions of several
variables that are multivariate regularly varying. Such functions behave
asymptotically as homogeneous functions. In the talk we discuss several
possible definitions and properties of multivariate regularly varying
functions. Next we discuss several possible applications such as
multivariate limit theorems for the partial sum or partial maxima of i.i.d.
random vectors, multivariate renewal theory, the difference between the
distribution functions of partial sums and partial maxima of random vectors.
Cetvrtak, 23. april 1998. u 12 h:
Dr Jurij Hohlov (Rusija): Stable Distributions and Their Applications
Stable distributions occur as the limit ones for normalized partial sums of
i.i.d. real-valued random variables. We consider various generalizations of
this scheme: semistable, operator stable distributions, stable and
semistable distributions on groups, pseudostable distributions in Gnedenko
problem and others. Special interest is the description of the domains of
attraction. Stable and semistable distributions are solutions of special
functional equation of convolution type. In multidimensional case the
solution of such equation is a very interesting open problem. We consider
some special cases.
Petak, 24. april 1998. u 11 h, Zajednicki sastanak Odeljenja za matematiku i
Seminara za stohastiku:
Dr Jurij Hohlov (Rusija): Some Problems in Financial Mathematics
The basic notions of financial mathematics. Binomial model of market with
two assets. Continuous-time models and their approximation by discrete-time
models. Option pricing. Cox-Ross-Rubinstein and Black-Scholes models. The
equivalence of binomial model and one with bounded changes in prices.
Heavy-tailed distributions: models and applications. Option pricing for
log-stable process for prices. Some open problems.
Slobodanka Jankovic i Drazen Pantic
rukovodioci seminara