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The Method of Upper and Lower Solutions of Stochastic Differential Equations and Applications
Authors:
Nikolaos Halidias a;
Mariusz Michta b
| Affiliations: | a Department of Statistics and Actuarial-Finance Mathematics, Laboratory of Actuarial-Financial Mathematics, University of the Aegean, Karlovassi, Samos, Greece |
b Faculty of Mathematics, Computer Science and Econometrics, University of Zielona G ra, Podgrna, Zielona Gra, Poland |
DOI:
10.1080/07362990701670217
Publication Frequency:
6 issues per year
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Abstract
The purpose of this article is to consider a stochastic integral equation driven by semimartingale with discontinuous and increasing drift part. We discuss the existence of strong solutions using lower and upper solutions method and a fixed point theorem for ordered topological space. Finally we present some applications in finance.
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| Keywords: Fixed points; Lower and upper solutions; Risk models; Semi martingales; Stochastic differential equations |
| AMS Subject Classification: 60H10; 60H20; 62P05 |
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