On strong solutions for positive definite jump diffusions

Eberhard Mayerhofer, Oliver Pfaffel and Robert Stelzer

Stochastic Processes and their Applications, 2011, vol. 121, issue 9, 2072-2086

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 [alpha]th positive semidefinite power of the process itself with 0.5

Keywords: 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 (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (17)

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