Seminar on Stohastics
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