Benutzer: Gast  Login
Dokumenttyp:
Zeitschriftenaufsatz 
Autor(en):
Mayerhofer, E., Pfaffel, O. and Stelzer, R. 
Titel:
On strong solutions for positive definite jump diffusions 
Abstract:
We show the existence of unique global strong solutions of a class of stochastic differential equations on the cone of symmetric positive definite matrices. Our result includes affine diffusion processes and therefore extends considerably the known statements concerning Wishart processes, which have recently been extensively employed in financial mathematics. Moreover, we consider stochastic differential equations where the diffusion coefficient is given by the αth positive semidefinite power of the process itself with 0.5<α<1 and obtain existence conditions for them. In the case of a diffusion coefficient which is linear in the process we likewise get a positive definite analogue of the univariate GARCH diffusions. 
Stichworte:
Affine diffusions; Jump diffusion processes on positive definite matrices; Local martingales on stochastic intervals; Matrix subordinators; Stochastic differential equations on open sets; Strong solutions; Wishart processes 
Zeitschriftentitel:
Stochastic Processes and their Applications 
Jahr:
2011 
Band / Volume:
121 
Heft / Issue:
Seitenangaben Beitrag:
2072–2086 
Reviewed:
ja 
Sprache:
en 
Status:
Verlagsversion / published 
TUM Einrichtung:
Lehrstuhl für Mathematische Statistik 
Format:
Text