Risk Analysis of Shanghai Inter-Bank Offered Rate - A GARCH-VaR Approach

The inter-bank offered rate widely used by Chinese commercial banks is Shanghai Inter-Bank Offered Rate (Shibor). Shibor has experienced significant development since it was created. It offers different products by duration. Despite its importance in China’s financial market, Shibor’s risk has largely remained unexplored. Making contribution to existing literature on risk management of Shibor, this paper investigates risk of Shanghai Inter- Bank Offered Rate (Shibor) utilizing GARCH-VaR method. The VaR of each product is calculated and compared while GARCH model is designed for a simpler calculation. In order to have a clearer view of Chinese commercial banks, the data selected is Shibor data sample from 2006 to 2016, which is measured by GARCH-VaR model and verified effectiveness by chi-square test. Empirical results show strong evidence for the need of Chinese commercial banks to change the status quo so that the great fluctuation and abnormal situation can be avoided. Policy implication, involving the interest rate management and internal problem in commercial banks, is proposed for financial regulators

Coverage Performance Analysis of Reconfigurable Intelligent Surface-aided Millimeter Wave Network with Blockage Effect

In order to solve spectrum resource shortage and satisfy immense wireless data traffic demands, millimeter wave (mmWave) frequency with large available bandwidth has been proposed for wireless communication in 5G and beyond 5G. However, mmWave communications are susceptible to blockages. This characteristic limits the network performance. Meanwhile, reconfigurable intelligent surface (RIS) has been proposed to improve the propagation environment and extend the network coverage. Unlike traditional wireless technologies that improve transmission quality from transceivers, RISs enhance network performance by adjusting the propagation environment. One of the promising applications of RISs is to provide indirect line-of-sight (LoS) paths when the direct LoS path between transceivers does not exist. This application makes RIS particularly useful in mmWave communications. With effective RIS deployment, the mmWave RIS-aided network performance can be enhanced significantly. However, most existing works have analyzed RIS-aided network performance without exploiting the flexibility of RIS deployment and/or considering blockage effect, which leaves huge research gaps in RIS-aided networks. To fill the gaps, this thesis develops RIS-aided mmWave network models considering blockage effect under the stochastic geometry framework. Three scenarios, i.e., indoor, outdoor and outdoor-to-indoor (O2I) RIS-aided networks, are investigated. Firstly, LoS propagation is hard to be guaranteed in indoor environments since blockages are densely distributed. Deploying RISs to assist mmWave transmission is a promising way to overcome this challenge. In the first paper, we propose an indoor mmWave RIS-aided network model capturing the characteristics of indoor environments. With a given base station (BS) density, whether deploying RISs or increasing BS density to further enhance the network coverage is more cost-effective is investigated. We present a coverage calculation algorithm which can be adapted for different indoor layouts. Then, we jointly analyze the network cost and coverage probability. Our results indicate that deploying RISs with an appropriate number of BSs is more cost-effective for achieving an adequate coverage probability than increasing BSs only. Secondly, for a given total number of passive elements, whether fewer large-scale RISs or more small-scale RISs should be deployed has yet to be investigated in the presence of the blockage effect. In the second paper, we model and analyze a 3D outdoor mmWave RIS-aided network considering both building blockages and human-body blockages. Based on the proposed model, the analytical upper and lower bounds of the coverage probability are derived. Meanwhile, the closed-form coverage probability when RISs are much closer to the UE than the BS is derived. In terms of coverage enhancement, we reveal that sparsely deployed large-scale RISs outperform densely deployed small-scale RISs in scenarios of sparse blockages and/or long transmission distances, while densely deployed small-scale RISs win in scenarios of dense blockages and/or short transmission distances. Finally, building envelope (the exterior wall of a building) makes outdoor mmWave BS difficult to communicate with indoor UE. Transmissive RISs with passive elements have been proposed to refract the signal when the transmitter and receiver are on the different side of the RIS. Similar to reflective RISs, the passive elements of a transmissive RIS can implement phase shifts and adjust the amplitude of the incident signals. By deploying transmissive RISs on the building envelope, it is feasible to implement RIS-aided O2I mmWave networks. In the third paper, we develop a 3D RIS-aided O2I mmWave network model with random indoor blockages. Based on the model, a closed-form coverage probability approximation considering blockage spatial correlation is derived, and multiple-RIS deployment strategies are discussed. For a given total number of RIS passive elements, the impact of blockage density, the number and locations of RISs on the coverage probability is analyzed. All the analytical results have been validated by Monte Carlo simulation. The observations from the result analysis provide guidelines for the future deployment of RIS-aided mmWave networks

Learning Predictive Safety Filter via Decomposition of Robust Invariant Set

Ensuring safety of nonlinear systems under model uncertainty and external disturbances is crucial, especially for real-world control tasks. Predictive methods such as robust model predictive control (RMPC) require solving nonconvex optimization problems online, which leads to high computational burden and poor scalability. Reinforcement learning (RL) works well with complex systems, but pays the price of losing rigorous safety guarantee. This paper presents a theoretical framework that bridges the advantages of both RMPC and RL to synthesize safety filters for nonlinear systems with state- and action-dependent uncertainty. We decompose the robust invariant set (RIS) into two parts: a target set that aligns with terminal region design of RMPC, and a reach-avoid set that accounts for the rest of RIS. We propose a policy iteration approach for robust reach-avoid problems and establish its monotone convergence. This method sets the stage for an adversarial actor-critic deep RL algorithm, which simultaneously synthesizes a reach-avoid policy network, a disturbance policy network, and a reach-avoid value network. The learned reach-avoid policy network is utilized to generate nominal trajectories for online verification, which filters potentially unsafe actions that may drive the system into unsafe regions when worst-case disturbances are applied. We formulate a second-order cone programming (SOCP) approach for online verification using system level synthesis, which optimizes for the worst-case reach-avoid value of any possible trajectories. The proposed safety filter requires much lower computational complexity than RMPC and still enjoys persistent robust safety guarantee. The effectiveness of our method is illustrated through a numerical example

Solving general elliptical mixture models through an approximate Wasserstein manifold

We address the estimation problem for general finite mixture models, with a particular focus on the elliptical mixture models (EMMs). Compared to the widely adopted Kullback-Leibler divergence, we show that the Wasserstein distance provides a more desirable optimisation space. We thus provide a stable solution to the EMMs that is both robust to initialisations and reaches a superior optimum by adaptively optimising along a manifold of an approximate Wasserstein distance. To this end, we first provide a unifying account of computable and identifiable EMMs, which serves as a basis to rigorously address the underpinning optimisation problem. Due to a probability constraint, solving this problem is extremely cumbersome and unstable, especially under the Wasserstein distance. To relieve this issue, we introduce an efficient optimisation method on a statistical manifold defined under an approximate Wasserstein distance, which allows for explicit metrics and computable operations, thus significantly stabilising and improving the EMM estimation. We further propose an adaptive method to accelerate the convergence. Experimental results demonstrate the excellent performance of the proposed EMM solver.Comment: This work has been accepted to AAAI2020. Note that this version also corrects a small error on the Equation (16) in proo

Safe Reinforcement Learning with Dual Robustness

Reinforcement learning (RL) agents are vulnerable to adversarial disturbances, which can deteriorate task performance or compromise safety specifications. Existing methods either address safety requirements under the assumption of no adversary (e.g., safe RL) or only focus on robustness against performance adversaries (e.g., robust RL). Learning one policy that is both safe and robust remains a challenging open problem. The difficulty is how to tackle two intertwined aspects in the worst cases: feasibility and optimality. Optimality is only valid inside a feasible region, while identification of maximal feasible region must rely on learning the optimal policy. To address this issue, we propose a systematic framework to unify safe RL and robust RL, including problem formulation, iteration scheme, convergence analysis and practical algorithm design. This unification is built upon constrained two-player zero-sum Markov games. A dual policy iteration scheme is proposed, which simultaneously optimizes a task policy and a safety policy. The convergence of this iteration scheme is proved. Furthermore, we design a deep RL algorithm for practical implementation, called dually robust actor-critic (DRAC). The evaluations with safety-critical benchmarks demonstrate that DRAC achieves high performance and persistent safety under all scenarios (no adversary, safety adversary, performance adversary), outperforming all baselines significantly