Προβλήματα martingales και αλλαγές μέτρων
Martingale problems and changes of measure
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Keywords
Martingales (Mathematics)Abstract
Let (Ω;F; F; P) be a filtered probability space. Which are all the probability measures
on F under which all the members of a given family X of processes are local
martingales? Such a problem is called a martingale-problem. First ′′general′′ martingale
problems are introduced, and then the martingale-problems related with point
processes, random measures and semi-martingales are investigated. Next, the
problem of what happens to a semi-martingale or a random measure, when one
replaces the original measure P by another probability measure Q on F which is
absolutely continuous with respect to P; is studied. Part of the problem consists
in various versions of Girsanov’s theorem. Another part examined, consists in
computing density processes. Solutions to the above problems have applications to
actuarial science and financial mathematics.
Postgraduate Studies Programme
Αναλογιστική Επιστήμη και Διοικητική ΚινδύνουDepartment
Σχολή Χρηματοοικονομικής και Στατιστικής. Τμήμα Στατιστικής και Ασφαλιστικής ΕπιστήμηςNumber of pages
190Language
GreekCollections
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Attribution-NonCommercial-NoDerivatives 4.0 Διεθνές
Attribution-NonCommercial-NoDerivatives 4.0 Διεθνές