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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
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Author, Monographic
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Title, Monographic
Advance in mathematics research
Reprint Status
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Edition
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Publisher Name
Nova science
Date of Publication
2004
Volume ID
6
Issue ID
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Page(s)
101-126
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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.....
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