A new mathematical method is proposed to convert the oscillator instability parameters from Allan variance to Spectrum Density(SD)of random phase fluctuations,which is the inversion of the classic transformation formu...A new mathematical method is proposed to convert the oscillator instability parameters from Allan variance to Spectrum Density(SD)of random phase fluctuations,which is the inversion of the classic transformation formula from SD to Allan variance.Due to the fact that Allan variance does not always determine a unique SD function,power-law model of the SD of oscillator phase fluctuations is introduced to the translating algorithm and a constrained maximum likelihood solution is presented.Considering that the inversion is an ill-posed problem,a regularization method is brought forward in the process.Simulation results show that the converted SD of phase fluctuations from Allan variance parameters agrees well with the real SD function.Furthermore,the effects of the selected regularization factors and the input Allan variances are analyzed in detail.展开更多
This paper considers the pricing of LIBOR futures in the Cox-Ingersoll-Ross(CIR)modelunder Pozdnyakov and Steele(2004)'s martingale framework for futures prices.Under the CIR modelfor short term interest rate,we p...This paper considers the pricing of LIBOR futures in the Cox-Ingersoll-Ross(CIR)modelunder Pozdnyakov and Steele(2004)'s martingale framework for futures prices.Under the CIR modelfor short term interest rate,we prove that there exists a unique futures price process associated withthe terminal value and the standard financial market,and that this unique futures price process has amartingale representation.Moreover,a general closed-form pricing formula for LIBOR futures contractsis obtained in the CIR model.展开更多
文摘A new mathematical method is proposed to convert the oscillator instability parameters from Allan variance to Spectrum Density(SD)of random phase fluctuations,which is the inversion of the classic transformation formula from SD to Allan variance.Due to the fact that Allan variance does not always determine a unique SD function,power-law model of the SD of oscillator phase fluctuations is introduced to the translating algorithm and a constrained maximum likelihood solution is presented.Considering that the inversion is an ill-posed problem,a regularization method is brought forward in the process.Simulation results show that the converted SD of phase fluctuations from Allan variance parameters agrees well with the real SD function.Furthermore,the effects of the selected regularization factors and the input Allan variances are analyzed in detail.
基金supported by the National Natural Science Foundation of China under Grant Nos.70971006,70501003,70831001the National Basic Research Program of China (973 Program) under Grant No.2007CB814906
文摘This paper considers the pricing of LIBOR futures in the Cox-Ingersoll-Ross(CIR)modelunder Pozdnyakov and Steele(2004)'s martingale framework for futures prices.Under the CIR modelfor short term interest rate,we prove that there exists a unique futures price process associated withthe terminal value and the standard financial market,and that this unique futures price process has amartingale representation.Moreover,a general closed-form pricing formula for LIBOR futures contractsis obtained in the CIR model.
