Publication Type
Book Chapter
UWI Author(s)
Author, Analytic
Rodkina, Alexandra E.; Mao, Xuerong
Author Affiliation, Ana.
Department of Mathematics and Computer Science
Title, Analytic
On asymptotic behaviour of solutions to nonlinear difference equation with nonmartingale type noise
Medium Designator
n/a
Connective Phrase
n/a
Author, Monographic
n/a
Author Role
n/a
Title, Monographic
Advance in mathematics research
Reprint Status
n/a
Edition
n/a
Place of Publication
n/a
Publisher Name
Nova science
Date of Publication
2004
Volume ID
6
Issue ID
n/a
Page(s)
101-126
Series Editor
n/a
Series Editor Role
n/a
Series Title
n/a
Series Volume Identification
n/a
Series Issue Identification
n/a
Connective Phrase
n/a
Location/URL
n/a
Notes
n/a
Abstract
A stochastic difference equation of the Volterra type driven by the martingale differences
i
xi+1 = Gi [xi, xi-1, . . . , x0] + fi [xi, xi-1, . . . , x0] +
k0 Xk=0
i-k [xi-k, xi-k-1, . . . , x0] i+1-k (1)
is considered . When k0 1 this equation cannot be treated as a stochastic equation with respect to a discrete semimartingale because the term Pk0 k=0 i-ki+1-k may not be a martingale-difference.
Eqn (1) can be interpreted as a generalization of the equation describing the
gain incurred by the insurance company in a year i + 1.
The sufficient conditions on asymptotic behaviours of the solution to Eqn (1)
are established. All conditions are expressed in terms of martingale-difference’s
characteristics. Special decompositions of the martingales were developed in
order to obtain our results.
A particular treatment of solutions in terms of increments of company surplus
is also given as an application of our theory.....
read more
read more
Keywords