Value-at-Risk （VaR） estimation via Monte Carlo （MC） simulation is studied here. The variance reduction technique is proposed in order to speed up MC algorithm. The algorithm for estimating the probability of high ...Value-at-Risk （VaR） estimation via Monte Carlo （MC） simulation is studied here. The variance reduction technique is proposed in order to speed up MC algorithm. The algorithm for estimating the probability of high portfolio losses （more general risk measure） based on the Cross - Entropy importance sampling is developed. This algorithm can easily be applied in any light- or heavy-tailed case without an extra adaptation. Besides, it does not loose in the performance in comparison to other known methods. A numerical study in both cases is performed and the variance reduction rate is compared with other known methods. The problem of VaR estimation using procedures for estimating the probability of high portfolio losses is also discussed.展开更多
Gaofen-3-02(GF3-02)is the first C-band synthetic aperture radar(SAR)satellite with terrain observation with progressive scans of SAR(TOPSAR)imaging mode in China,which plays an essential role in marine environment mon...Gaofen-3-02(GF3-02)is the first C-band synthetic aperture radar(SAR)satellite with terrain observation with progressive scans of SAR(TOPSAR)imaging mode in China,which plays an essential role in marine environment monitoring.Given the weak scattering characteristics of the ocean,the system thermal noise superimposed on SAR images has significant interference,especially in cross-polarization channels.Noise-Equivalent Sigma-Zero(NESZ)is a measure of the sensitivity of the radar to areas of low backscatter.The NESZ is defined to be the scattering cross-section coefficient of an area which contributes a mean level in the image equal to the signal-independent additive noise level.For TOPSAR,NESZ exhibits the shape of the SAR scanning gain curve in the azimuth and the shape of the antenna pattern in the range.Therefore,the accurate measurement of NESZ plays a vital role in the application of spaceborne SAR sea surface cross-polarization data.This paper proposes a theoretical calculation method for the NESZ curve in GF3-02 TOPSAR mode based on SAR noise inner calibration data and the imaging algorithm.A method for correcting the error existing in the theoretical curve of NESZ is also proposed according to the relationship between sea surface backscattering and wind speed and the same characteristics of target scattering in the overlapping area of adjacent sub-swaths.According to assessment with wide-swath TOPSAR cross-polarization data,the GF3-02 TOPSAR mode has a very low thermal noise level,which is better than−33 dB at the edge of each beam,and controlled below−38 dB at the center of the beam.The two-dimensional reference curves of the NESZ of each beam are provided to the GF3-02 TOPSAR users.After discussing the relationship between normalized radar cross section(NRCS)and wind speed,we provide a formula for NRCS related to wind speed and radar incidence angle.Compared with the NRCS derived from this formula and the NESZ-subtracted NRCS of SAR images,the bias is−0.0048 dB,the Root Mean Square Error is 1.671 dB and the correlation coefficient is 0.939.展开更多
文摘Value-at-Risk （VaR） estimation via Monte Carlo （MC） simulation is studied here. The variance reduction technique is proposed in order to speed up MC algorithm. The algorithm for estimating the probability of high portfolio losses （more general risk measure） based on the Cross - Entropy importance sampling is developed. This algorithm can easily be applied in any light- or heavy-tailed case without an extra adaptation. Besides, it does not loose in the performance in comparison to other known methods. A numerical study in both cases is performed and the variance reduction rate is compared with other known methods. The problem of VaR estimation using procedures for estimating the probability of high portfolio losses is also discussed.
基金The National Natural Science Foundation of China under contract No.41976169.
文摘Gaofen-3-02(GF3-02)is the first C-band synthetic aperture radar(SAR)satellite with terrain observation with progressive scans of SAR(TOPSAR)imaging mode in China,which plays an essential role in marine environment monitoring.Given the weak scattering characteristics of the ocean,the system thermal noise superimposed on SAR images has significant interference,especially in cross-polarization channels.Noise-Equivalent Sigma-Zero(NESZ)is a measure of the sensitivity of the radar to areas of low backscatter.The NESZ is defined to be the scattering cross-section coefficient of an area which contributes a mean level in the image equal to the signal-independent additive noise level.For TOPSAR,NESZ exhibits the shape of the SAR scanning gain curve in the azimuth and the shape of the antenna pattern in the range.Therefore,the accurate measurement of NESZ plays a vital role in the application of spaceborne SAR sea surface cross-polarization data.This paper proposes a theoretical calculation method for the NESZ curve in GF3-02 TOPSAR mode based on SAR noise inner calibration data and the imaging algorithm.A method for correcting the error existing in the theoretical curve of NESZ is also proposed according to the relationship between sea surface backscattering and wind speed and the same characteristics of target scattering in the overlapping area of adjacent sub-swaths.According to assessment with wide-swath TOPSAR cross-polarization data,the GF3-02 TOPSAR mode has a very low thermal noise level,which is better than−33 dB at the edge of each beam,and controlled below−38 dB at the center of the beam.The two-dimensional reference curves of the NESZ of each beam are provided to the GF3-02 TOPSAR users.After discussing the relationship between normalized radar cross section(NRCS)and wind speed,we provide a formula for NRCS related to wind speed and radar incidence angle.Compared with the NRCS derived from this formula and the NESZ-subtracted NRCS of SAR images,the bias is−0.0048 dB,the Root Mean Square Error is 1.671 dB and the correlation coefficient is 0.939.
