Serdica Mathematical Journal
Volume 29, Number 3, 2003
C O N T E N T S
A B S T R A C T S
AN APPROACH TO WEALTH MODELLING
Pavel Stoynov
todorov@fmi.uni-sofia.bg,
todorov@feb.uni-sofia.bg
2000 Mathematics Subject Classification:
60G48, 60G20, 60G15, 60G17.
Key words:
Wealth Motion Models, generalized Lévy process,
Brownian motion with returns to zero.
The change in the wealth of a market agent (an investor, a company,
a bank etc.) in an economy is a popular topic in finance. In this paper,
we propose a general stochastic model describing the wealth process and
give some of its properties and special cases. A result regarding the
probability of
default within the framework of the model is also offered.
SUFFICIENT SECOND ORDER OPTIMALITY CONDITIONS
FOR C^{1} MULTIOBJECTIVE OPTIMIZATION PROBLEMS
N. Gadhi
n.gadhi@ucam.ac.ma
2000 Mathematics Subject Classification:
Primary 90C29; Secondary 90C30.
Key words:
Approximate Hessian matrix, Recession
matrices, Sufficient second order optimality conditions, Support functions,
Multiobjective optimization.
In this work, we use the notion of Approximate
Hessian introduced by Jeyakumar and Luc [19], and a special
scalarization to establish sufficient optimality conditions for constrained
multiobjective optimization problems. Throughout this paper, the data are
assumed to be of class C^{1}, but not necessarily of class C^{1.1}.
UPPER AND LOWER BOUNDS IN RELATOR SPACES
Árpád Száz
szaz@math.klte.hu
2000 Mathematics Subject Classification:
06A06, 54E15.
Key words:
Relational systems, interiors and closures, upper and lower
bounds, maxima and minima.
An ordered pair X(Â) = (X, Â)
consisting of a nonvoid set X and a nonvoid family Â
of binary relations on X is called a relator space. Relator spaces
are straightforward generalizations not only of uniform spaces,
but also of ordered sets.
Therefore, in a relator space we can naturally define not only
some topological notions, but also some order theoretic ones.
It turns out that these two, apparently quite different, types of
notions are closely related to each other through complementations.
A NEW ALGORITHM FOR MONTE CARLO FOR AMERICAN OPTIONS
Roland Mallier
mallier@uwo.ca,
Ghada Alobaidi
galobaidi@aus.ac.ae
2000 Mathematics Subject Classification:
91B28, 65C05.
Key words:
American options; Monte Carlo.
We consider the valuation of American options using Monte Carlo
simulation, and propose a new technique which involves
approximating the optimal exercise boundary.
Our method involves
splitting the boundary into a linear term and a Fourier
series and using stochastic optimization in the form of
a relaxation method to calculate
the coefficients in the series.
The cost function used is the expected value of the option using the
the current estimate of the location of the boundary.
We present some sample results and compare our results to other methods.
THE VARIETY OF LEIBNIZ ALGEBRAS DEFINED BY THE IDENTITY
x(y(zt)) º 0
L. E. Abanina
nla@mail.ru,
S. P. Mishchenko
mishchenkosp@ulsu.ru
2000 Mathematics Subject Classification:
Primary: 17A32; Secondary: 16R10, 16P99, 17B01, 17B30, 20C30.
Key words:
Leibniz algebras with polynomial identities, varieties of
Leibniz algebras, codimensions, colength, multiplicities.
Let F be a field of characteristic zero. In this paper we study
the variety of Leibniz algebras _{3} N
determined by the identity x(y(zt)) º 0.
The algebras of this
variety are left nilpotent of class not more than 3. We give a
complete description of the vector space of multilinear identities in the
language of representation theory of the symmetric group S_{n}
and Young diagrams. We also show that the variety _{3} N
is generated by an abelian extension of the Heisenberg Lie algebra.
It has turned out that _{3} N has many properties which are
similar to the properties of the variety of the
abelian-by-nilpotent of class 2 Lie algebras. It has overexponential
growth of the codimension sequence and subexponential growth of the
colength sequence.
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