Sensitivity of the Eisenberg-Noe clearing vector to individual interbank liabilities

We quantify the sensitivity of the Eisenberg-Noe clearing vector to estimation errors in the bilateral liabilities of a financial system in a stylized setting. The interbank liabilities matrix is a crucial input to the computation of the clearing vector. However, in practice central bankers and regulators must often estimate this matrix because complete information on bilateral liabilities is rarely available. As a result, the clearing vector may suffer from estimation errors in the liabilities matrix. We quantify the clearing vector's sensitivity to such estimation errors and show that its directional derivatives are, like the clearing vector itself, solutions of fixed point equations. We describe estimation errors utilizing a basis for the space of matrices representing permissible perturbations and derive analytical solutions to the maximal deviations of the Eisenberg-Noe clearing vector. This allows us to compute upper bounds for the worst case perturbations of the clearing vector in our simple setting. Moreover, we quantify the probability of observing clearing vector deviations of a certain magnitude, for uniformly or normally distributed errors in the relative liability matrix. Applying our methodology to a dataset of European banks, we find that perturbations to the relative liabilities can result in economically sizeable differences that could lead to an underestimation of the risk of contagion. Our results are a first step towards allowing regulators to quantify errors in their simulations.Comment: 37 page

In the Wake of the Financial Crisis - Regulators' and Investors' Perspectives

Before the 2008 financial crisis, most research in financial mathematics focused on the risk management and the pricing of options without considering effects of counterparties' default, illiquidity problems, systemic risk and the role of the repurchase agreement (Repo). During the 2008 financial crisis, a frozen Repo market led to a shutdown of short sales in the stock market. Cyclical interdependencies among financial corporations caused that a default of one firm seriously affected other firms and even the whole financial network.\nIn this dissertation, we will consider financial markets which are shaped by financial crisis. This will be done from two distinct perspectives, an investor's and a regulator's. From an investor's perspective, recently models were proposed to compute the total valuation adjustment (XVA) of derivatives without considering a potential crisis in the market. In our research, we include a possible crisis by apply an alternating renewal process to describe a switching between a normal financial status and a financial crisis status. We develop a framework for pricing the XVA of a European claim in this state-dependent framework. We represent the price as a solution to a backward stochastic differential equation and prove the existence and uniqueness of the solution.\nTo study financial networks from a regulator's perspective, one popular method is the fixed point based approach by L. Eisenberg and T. Noe. However, in practice, there is no accurate record of the interbank liabilities and thus one has to estimate them to use Eisenberg - Noe type models. In our research, we conduct a sensitivity analysis of the Eisenberg - Noe framework, and quantify the effect of the estimation errors to the clearing payments. We show that the effect of the missing specification of interbank connection to clearing payments can be described via directional derivatives that can be represented as solutions of fixed point equations. We also compute the probability of observing clearing payment deviations of a certain magnitude

Direct Probability Integral Method for Seismic Performance Assessment of Earth Dam Subjected to Stochastic Mainshock–Aftershock Sequences

Studying the impact of mainshock–aftershock sequences on dam reliability is crucial for effective disaster prevention measures. With this purpose in mind, a new method for stochastic dynamic response analyses and reliability assessments of dams during seismic sequences has been proposed. Firstly, a simulation method of stochastic seismic sequences is described, considering the dependence between mainshock and aftershock based on Copula function. Then, a novel practical framework for stochastic dynamic analysis is established, combined with the improved point selection strategy and the direct probability integration method (DPIM). The DPIM is employed on a nonlinear system with one degree of freedom and compared with Monte Carlo simulation (MCS). The findings reveal that the method boasts exceptional precision and efficiency. Finally, the seismic performance of a practical dam was evaluated based on the above method, which not only accurately estimates the response probability distribution and dynamic reliability of the dam, but also greatly reduces the required calculations. Furthermore, the impact of aftershocks on dam seismic performance is initially evaluated through a probability approach in this research. It is found that seismic sequences will significantly increase the probability of earth dam failure compared with sequences of only mainshocks. In addition, the influence of aftershocks on reliability will further increase when the limit state is more stringent. Specifically, the novel analysis method proposed in this paper provides more abundant and objective evaluation indices, providing a dynamic reliability assessment for dams that is more effective than traditional evaluation methods

Magnetically Suspended Control Sensitive Gyroscope Rotor High-Precision Deflection Decoupling Method using Quantum Neural Network and Fractional-Order Terminal Sliding Mode Control

To achieve high-precision deflection control of a Magnetically Suspended Control and Sensitive Gyroscope rotor under high dynamic conditions, a deflection decoupling method using Quantum Radial Basis Function Neural Network and fractional-order terminal sliding mode control is proposed. The convergence speed and time complexity of the neural network controller limit the control accuracy and stability of rotor deflection under high-bandwidth conditions. To solve the problem, a quantum-computing-based structure optimization method for the Radial Basis Function Neural Network is proposed for the first time, where the input and the center of hidden layer basis function of the neural network are quantum-coded, and quantum rotation gates are designed to replace the Gaussian function. The parallel characteristic of quantum computing is utilized to reduce the time complexity and improve the convergence speed of the neural network. On top of that, in order to further address the issue of input jitter, a fractional-order terminal sliding mode controller based on the Quantum Radial Basis Function Neural Network is designed, the fractional-order differential sliding mode surface and the fractional-order convergence law are proposed to reduce the input jitter and achieve finite-time convergence of the controller, and the Quantum Radial Basis Function Neural Network is used to approximate the residual coupling and external disturbances of the system, resulting in improving the rotor deflection control accuracy. The semi-physical simulation experiments demonstrate the effectiveness and superiority of the proposed method

Facile Route for Bio-Phenol Siloxane Synthesis via Heterogeneous Catalytic Method and its Autonomic Antibacterial Property

Eugenol, used as bio-phenol, was designed to replace the hydrogen atom of hydrogenterminated siloxane by hydrosilylation reaction under the presence of alumina-supported platinum catalyst (Pt-Al2O3), silica-supported platinum catalyst (Pt-SiO2) and carbon nanotube-supported platinum catalyst (Pt-CNT), respectively. The catalytic activities of these three platinum catalysts were measured by nuclear magnetic resonance hydrogen spectrometer (1H NMR). The properties of bio-phenol siloxane were characterized by Fourier transform infrared spectrometer (FT–IR), UV-visible spectrophotometer (UV) and thermogravimeter (TGA), and its antibacterial property against Escherichia coli was also studied. The results showed that the catalytic activity of the catalyst Pt-CNT was preferable. When the catalyst concentration was 100 ppm, the reaction temperature was 80 °C and reaction time was 6 h, the reactant conversion rate reached 97%. After modification with bio-phenol, the thermal stability of the obtained bio-phenol siloxane was improved. For bio-phenol siloxane, when the ratio of weight loss reached 98%, the pyrolysis temperature was raised to 663 °C which was 60 °C higher than hydrogenterminated siloxane. Meanwhile, its autonomic antibacterial property against Escherichia coli was improved significantly

Bioinformatics Analysis of DNA-binding Response Regulator PhoP in Vibrio alginolyticus

[Objectives] To amplify the DNA-binding response regulator PhoP in Vibrio alginolyticus and analyze its sequence characteristics and subunit structure. [Methods] According to the sequence of the DNA-binding response regulator PhoP in V. alginolyticus, a pair of specific primers was designed for PCR amplification, and the bioinformatics of the sequence amplified was analyzed. Using MEGA 5.0 software, the phoP phylogenetic tree was constructed by the neighbor-joining method. Using SWISS-MODEL software, the three-dimensional structural model of the PhoP subunit was simulated. [Results] The full-length phoP gene was 732 bp, encoding a total of 243 amino acids. The predicted theoretical molecular weight of the protein is about 27.67 kD, and the isoelectric point is 5.09. The prediction results of protein subcellular localization, SignalP 4.0, TMHMM Server 2.0 and SoftBerry-Psite show that PhoP is located in the cytoplasm, and is stable and hydrophobic; there is a signal peptide cleavage site between amino acids 29 and 30, and there is no transmembrane region. The amino acid sequence contains one Asn-glycosylation site, one protein kinase C phosphorylation site, seven casein kinase II phosphorylation sites, one tyrosine kinase phosphorylation site, three myristoylation sites, and seven C-terminal microbody targeting signal sites. The PhoP of V. alginolyticus has high homology with that of Vibrio campbellii. The PhoP subunit of V. alginolyticus has similar configuration to the single-subunit RegX3 protein of Mycobacterium tuberculosis. [Conclusions] This study has a positive effect on the prevention and control of vibriosis and the improvement of the current aquatic economic animal breeding environment