Quantitative Analysis of Extreme Risks and Extremal Dependence in Insurance and Finance

In this thesis, we aim at a quantitative understanding of extreme risks and extremal depen- dence in insurance and finance. We use regularly varying distribution functions in extreme value theory (EVT) to model extreme risks, and apply various tools in multivariate extreme value theory (MEVT) to capture extremal dependence. We focus on developing asymptotics for certain risk measures. We start with a portfolio diversification problem. In finance, investors usually construct a mixed portfolio in order to diversify away the individual risks. However, this is not always the case when heavy-tailedness and tail dependence of large losses are considered. Chapter 3 applies the multivariate regular variation (MRV) model to study this problem in an asymptotic sense and provides an applicable portfolio optimization strategy. A practical performance test for our strategy is also provided in this Chapter. The mainstream of the literature on the limitation of portfolio diversification follows the assumption that risks have unbounded distribution support, i.e., no cap for potential loss. However, real-world firms usually have limited liability. Then a natural question arises whether the non-diversification effect strictly depends on the tail behaviour of the loss distribution. For risks with bounded support, will similar non-diversification results still exist? We answer this question in Chapter 4 and we argue that diversification is still possible to be inferior as long as the risks are truncated at sufficiently large threshold level. In Chapter 5, we consider the risk of a large credit portfolio of multiple obligors subject to possible default. Contrary to the Gaussian and t copulas that are widely used in practice, we assume a portfolio dependence structure of Archimedean copula type. Under this setting, we derive sharp asymptotics for portfolio credit risk that highlight the impact of extremal dependence among obligors. By utilizing these asymptotic results, we propose two different algorithms that are shown to be asymptotically optimal and can be applied to efficiently estimate portfolio credit risk via Monte Carlo simulation. In order to capture hierarchical dependence structure among the obligors in a large credit portfolio, we also extend our asymptotic analysis to the structure of nested Gumbel copulas and an efficient algorithm of bounded relative error is also developed for this more complex structure. Numerical results are provided at the end of the chapter to illustrate the performance of our algorithms, as well as their respective merits

Asymptotic analysis of portfolio diversification

In this paper, we investigate the optimal portfolio construction aiming at extracting the most diversification benefit. We employ the diversification ratio based on the Value-at-Risk as the measure of the diversification benefit. With modeling the dependence of risk factors by the multivariate regularly variation model, the most diversified portfolio is obtained by optimizing the asymptotic diversification ratio. Theoretically, we show that the asymptotic solution is a good approximation to the finite-level solution. Our theoretical results are supported by extensive numerical examples. By applying our portfolio optimization strategy to real market data, we show that our strategy provides a fast algorithm for handling a large portfolio, while outperforming other peer strategies in out-of-sample risk analyses.</p

Hidden non-collinear spin-order induced topological surface states

Rare-earth monopnictides are a family of materials simultaneously displaying complex magnetism, strong electronic correlation, and topological band structure. The recently discovered emergent arc-like surface states in these materials have been attributed to the multi-wave-vector antiferromagnetic order, yet the direct experimental evidence has been elusive. Here we report the observation of non-collinear antiferromagnetic order with multiple modulations using spin-polarized scanning tunneling microscopy. Moreover, we discover a hidden spin-rotation transition of single-to-multiple modulations 2 K below the Neel temperature. The hidden transition coincides with the onset of the surface states splitting observed by our angle-resolved photoemission spectroscopy measurements. Single modulation gives rise to a band inversion with induced topological surface states in a local momentum region while the full Brillouin zone carries trivial topological indices, and multiple modulation further splits the surface bands via non-collinear spin tilting, as revealed by our calculations. The direct evidence of the non-collinear spin order in NdSb not only clarifies the mechanism of the emergent topological surface states, but also opens up a new paradigm of control and manipulation of band topology with magnetism.Comment: 32 pages, 4 figures, 10 extended figure

Asymptotic analysis of portfolio diversification

In this paper, we investigate the optimal portfolio construction aiming at extracting the most diversification benefit. We employ the diversification ratio based on the Value-at-Risk as the measure of the diversification benefit. With modeling the dependence of risk factors by the multivariate regularly variation model, the most diversified portfolio is obtained by optimizing the asymptotic diversification ratio. Theoretically, we show that the asymptotic solution is a good approximation to the finite-level solution. Our theoretical results are supported by extensive numerical examples. By applying our portfolio optimization strategy to real market data, we show that our strategy provides a fast algorithm for handling a large portfolio, while outperforming other peer strategies in out-of-sample risk analyses

Machine-learning reprogrammable metasurface imager

Conventional imagers require time-consuming data acquisition, or complicated reconstruction algorithms for data post-processing. Here, the authors demonstrate a real-time digital-metasurface imager that can be trained in-situ to show high accuracy image coding and recognition for various image sets

Microwave Speech Recognizer Empowered by a Programmable Metasurface

International audienceSpeech recognition becomes increasingly important in the modern society, especially for human–machine interactions, but its deployment is still severely thwarted by the struggle of machines to recognize voiced commands in challenging real‐life settings: oftentimes, ambient noise drowns the acoustic sound signals, and walls, face masks or other obstacles hide the mouth motion from optical sensors. To address these formidable challenges, an experimental prototype of a microwave speech recognizer empowered by programmable metasurface is presented here that can remotely recognize human voice commands and speaker identities even in noisy environments and if the speaker&amp;amp;#039;s mouth is hidden behind a wall or face mask. The programmable metasurface is the pivotal hardware ingredient of the system because its large aperture and huge number of degrees of freedom allows the system to perform a complex sequence of sensing tasks, orchestrated by artificial‐intelligence tools. Relying solely on microwave data, the system avoids visual privacy infringements. The developed microwave speech recognizer can enable privacy‐respecting voice‐commanded human–machine interactions is experimentally demonstrated in many important but to‐date inaccessible application scenarios. The presented strategy will unlock new possibilities and have expectations for future smart homes, ambient‐assisted health monitoring, as well as intelligent surveillance and security

Microwave Speech Recognizer Empowered by a Programmable Metasurface

We present an experimental prototype of a microwave speech recognizer empowered by a programmable metasurface that can recognize voice commands and speaker identities remotely even in noisy environments and if the speaker’s mouth is hidden behind a wall or face mask. Thereby, we enable voice-commanded human machine interactions in many important but to-date inaccessible application scenarios, including smart health careand factory scenarios. The programmable metasurface is the pivotal hardware ingredient of our system because its large aperture and huge number of degrees of freedom allows our system to perform a complex sequence of tasks, orchestrated by artificial-intelligence tools. First, the speaker’s mouth is localized by imaging the scene and identifying the region of interest. Second, microwaves are efficiently focused on the speaker’s mouth toencode information about the vocalized speech in reflected microwave biosignals. The efficient focusing on the speaker’s mouth is the origin of our system’s robustness to various types of parasitic motion. Third, a dedicated neural network directly retrieves the sought-after speech information from the measured microwave biosignals. Relying solely on microwave data, our system avoids visual privacy infringements. We expect that thepresented strategy will unlock new possibilities for future smart homes, ambient-assisted health monitoring and care, smart factories, as well as intelligent surveillance and security