scholarly journals Martingale Problems for Conditional Distributions of Markov Processes

1998 ◽  
Vol 3 (0) ◽  
Author(s):  
Thomas Kurtz
Keyword(s):  
Markov Processes ◽  
Conditional Distributions ◽  
Martingale Problems

scholarly journals On characterisation of Markov processes via martingale problems

2006 ◽  
Vol 116 (1) ◽  
pp. 83-96
Author(s):  
Abhay G. Bhatt ◽  
Rajeeva L. Karandikar ◽  
B. V. Rao
Keyword(s):  
Markov Processes ◽  
Martingale Problems

Conditional Distributions of Processes Related to Fractional Brownian Motion

2013 ◽  
Vol 50 (01) ◽  
pp. 166-183 ◽  
Author(s):  
Holger Fink ◽  
Claudia Klüppelberg ◽  
Martina Zähle
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Markov Processes ◽  
Bond Market ◽  
Market Model ◽  
Standard Brownian Motion ◽  
Conditional Distributions ◽  
Prediction Formula ◽  
Defaultable Bond ◽  
The Core

Conditional distributions for affine Markov processes are at the core of present (defaultable) bond pricing. There is, however, evidence that Markov processes may not be realistic models for short rates. Fractional Brownian motion (FBM) can be introduced by an integral representation with respect to standard Brownian motion. Using a simple prediction formula for the conditional expectation of an FBM and its Gaussianity, we derive the conditional distributions of FBM and related processes. We derive conditional distributions for fractional analogies of prominent affine processes, including important examples like fractional Ornstein–Uhlenbeck or fractional Cox–Ingersoll–Ross processes. As an application, we propose a fractional Vasicek bond market model and compare prices of zero-coupon bonds to those achieved in the classical Vasicek model.

scholarly journals Conditional Distributions of Processes Related to Fractional Brownian Motion

2013 ◽  
Vol 50 (1) ◽  
pp. 166-183 ◽  
Author(s):  
Holger Fink ◽  
Claudia Klüppelberg ◽  
Martina Zähle
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Markov Processes ◽  
Bond Market ◽  
Market Model ◽  
Standard Brownian Motion ◽  
Conditional Distributions ◽  
Prediction Formula ◽  
Defaultable Bond ◽  
The Core

Conditional distributions for affine Markov processes are at the core of present (defaultable) bond pricing. There is, however, evidence that Markov processes may not be realistic models for short rates. Fractional Brownian motion (FBM) can be introduced by an integral representation with respect to standard Brownian motion. Using a simple prediction formula for the conditional expectation of an FBM and its Gaussianity, we derive the conditional distributions of FBM and related processes. We derive conditional distributions for fractional analogies of prominent affine processes, including important examples like fractional Ornstein–Uhlenbeck or fractional Cox–Ingersoll–Ross processes. As an application, we propose a fractional Vasicek bond market model and compare prices of zero-coupon bonds to those achieved in the classical Vasicek model.

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