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Ergodicity properties of affine term structure models and applications / von: Chiraz Trabelsi. Wuppertal, Juni 2016
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Short term Interest rate models
Cox-Ingersoll-Ross model
Mean reversion of the CIR model
Transition density function of the CIR process
Basic affine jump diffusion process
Jump-diffusion CIR process
Ergodic results on transformation of the CIR and application
Affine and regularity properties
Affine property
Regularity property
Positive Harris recurrence
Ergodicity results
Application in one credit migration model
Positive Harris recurrence, exponential ergodicity and calibration of the BAJD
Characteristic function of the BAJD
Mixtures of Bessel distributions
Transition density of the BAJD
Case i): >0
Case ii): <0
Case iii): =0
Positive Harris recurrence of the BAJD
Exponential ergodicity of the BAJD
Calibration for the BAJD-process
Exponential Ergodicity of the Jump-Diffusion CIR Process
Characteristic function of the JCIR
Special Case i): = 0, No Jumps
Special Case ii): =0 and x=0
Lower bound for the transition densities of JCIR
Exponential ergodicity of JCIR
Non affine term structure models
Connection between OU-process and CIR-process in the jumps case
Some investigations