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Affine processes on positive semidefinite matrices. (English) Zbl 1219.60068
The paper provides the systematic mathematical foundation for stochastically continuous affine processes on the cone of positive semidefinite symmetric matrices. Such processes have arisen from a large and growing range of applications in finance, including multi-asset option pricing with stochastic volatility and correlation structures, and fixed-income models with stochastically correlated risk factors and default intensities. Definition and characterization of affine processes are introduced and it is proved that affine processes are regular and Feller. Sufficient conditions on the parameters supplying the existence and uniqueness of affine process with the given generator are formulated. The realization of affine process as a jump-diffusion process is discussed.

MSC:
60J25 Continuous-time Markov processes on general state spaces
91B70 Stochastic models in economics
60J75 Jump processes (MSC2010)
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