A compact temperature-compensated fibre optic magnetic field sensor based on a self-referenced anti-resonant reflecting optical waveguide is proposed and experimentally demonstrated. Two hollow holes in the air ring cladding of the hollow core photonic crystal fibre (HCPCF) are infiltrated with magnetic fluid and ethanol. A self-referenced anti-resonant reflecting optical waveguide is formed in the cladding of the HCPCF between the magnetic fluid- and ethanol-infiltrated resonators. The applied magnetic field only changes the resonance condition of the magnetic fluid-infiltrated resonator, while the temperature influences the resonance conditions of both the magnetic fluid- and ethanol-infiltrated resonators simultaneously. Therefore, the proposed self-referenced anti-resonant reflecting optical waveguide can measure the magnetic field without temperature cross-sensitivity. The experimental results show that a magnetic field sensitivity of 81 pm/Oe can be achieved, and the standard variation of the wavelength difference is only 0.02 nm in the temperature range of 30 to 80 °C.
The paper studies derivative asset analysis in structural credit risk models where the asset value of the firm is not fully observable. It is shown that in order to determine the price dynamics of traded securities, one needs to solve a stochastic filtering problem for the asset value. We transform this problem to a filtering problem for a stopped diffusion process and apply results from the filtering literature to this problem. In this way, we obtain an stochastic partial differential equation characterization for the filter density. Moreover, we characterize the default intensity under incomplete information and determine the price dynamics of traded securities. Armed with these results, we study derivative assets in our setup: We explain how the model can be applied to the pricing of options on traded assets and we discuss dynamic hedging and model calibration. The paper closes with a small simulation study.
K E Y W O R D Sderivative asset analysis for corporate securities, incomplete information, stochastic filtering, structural credit risk models 84
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