Anomaly detection is an important problem that has been researched within diverse research areas and application domains. Many anomaly detection techniques have been specifically developed for certain application domains, while others are more generic. This survey tries to provide a structured and comprehensive overview of the research on anomaly detection. We have grouped existing techniques into different categories based on the underlying approach adopted by each technique. For each category we have identified key assumptions, which are used by the techniques to differentiate between normal and anomalous behavior. When applying a given technique to a particular domain, these assumptions can be used as guidelines to assess the effectiveness of the technique in that domain. For each category, we provide a basic anomaly detection technique, and then show how the different existing techniques in that category are variants of the basic technique. This template provides an easier and more succinct understanding of the techniques belonging to each category. Further, for each category, we identify the advantages and disadvantages of the techniques in that category. We also provide a discussion on the computational complexity of the techniques since it is an important issue in real application domains. We hope that this survey will provide a better understanding of the different directions in which research has been done on this topic, and how techniques developed in one area can be applied in domains for which they were not intended to begin with.

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Anomaly detection: A survey

Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

Convergence of Probability Measures

Quantum key distribution (QKD) is the first quantum information task to reach the level of mature technology, already fit for commercialization. It aims at the creation of a secret key between authorized partners connected by a quantum channel and a classical authenticated channel. The security of the key can in principle be guaranteed without putting any restriction on an eavesdropper's power. This article provides a concise up-to-date review of QKD, biased toward the practical side. Essential theoretical tools that have been developed to assess the security of the main experimental platforms are presented (discrete-variable, continuous-variable, and distributed-phase-reference protocols).

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The security of practical quantum key distribution

Economic Control of Quality of Manufactured Product.

This book provides the most comprehensive treatment of the theoretical concepts and modelling techniques of quantitative risk management. Whether you are a financial risk analyst, actuary, regulator or student of quantitative finance, Quantitative Risk Management gives you the practical tools you need to solve real-world problems. Describing the latest advances in the field, Quantitative Risk Management covers the methods for market, credit and operational risk modelling. It places standard industry approaches on a more formal footing and explores key concepts such as loss distributions, risk measures and risk aggregation and allocation principles. The book's methodology draws on diverse quantitative disciplines, from mathematical finance and statistics to econometrics and actuarial mathematics. A primary theme throughout is the need to satisfactorily address extreme outcomes and the dependence of key risk drivers. Proven in the classroom, the book also covers advanced topics like credit derivatives. Fully revised and expanded to reflect developments in the field since the financial crisis Features shorter chapters to facilitate teaching and learning Provides enhanced coverage of Solvency II and insurance risk management and extended treatment of credit risk, including counterparty credit risk and CDO pricing Includes a new chapter on market risk and new material on risk measures and risk aggregation

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Quantitative Risk Management: Concepts, Techniques, and Tools

We consider a single-product revenue management problem where, given an initial inventory, the objective is to dynamically adjust prices over a finite sales horizon to maximize expected revenues. Realized demand is observed over time, but the underlying functional relationship between price and mean demand rate that governs these observations (otherwise known as the demand function or demand curve) is not known. We consider two instances of this problem: (i) a setting where the demand function is assumed to belong to a known parametric family with unknown parameter values; and (ii) a setting where the demand function is assumed to belong to a broad class of functions that need not admit any parametric representation. In each case we develop policies that learn the demand function “on the fly,” and optimize prices based on that. The performance of these algorithms is measured in terms of the regret: the revenue loss relative to the maximal revenues that can be extracted when the demand function is known prior to the start of the selling season. We derive lower bounds on the regret that hold for any admissible pricing policy, and then show that our proposed algorithms achieve a regret that is “close” to this lower bound. The magnitude of the regret can be interpreted as the economic value of prior knowledge on the demand function, manifested as the revenue loss due to model uncertainty.

/pdf/dynamic-pricing-without-knowing-the-demand-function-risk-3afky4ow1g.pdf

Dynamic Pricing Without Knowing the Demand Function: Risk Bounds and Near-Optimal Algorithms

We consider a single product revenue management problem where, given an initial inventory, the objective is to dynamically adjust prices over a finite sales horizon to maximize expected revenues. Realized demand is observed over time, but the underlying functional relationship between price and mean demand rate that governs these observations (otherwise known as the demand function or demand curve), is not known. We consider two instances of this problem: i.) a setting where the demand function is assumed to belong to a known parametric family with unknown parameter values; and ii.) a setting where the demand function is assumed to belong to a broad class of functions that need not admit any parametric representation. In each case we develop policies that learn the demand function "on the fly," and optimize prices based on that. The performance of these algorithms is measured in terms of the regret: the revenue loss relative to the maximal revenues that can be extracted when the demand function is known prior to the start of the selling season. We derive lower bounds on the regret that hold for any admissible pricing policy, and then show that our proposed algorithms achieve a regret that is "close" to this lower bound. The magnitude of the regret can be interpreted as the economic value of prior knowledge on the demand function; manifested as the revenue loss due to model uncertainty.

In a multi-armed bandit (MAB) problem a gambler needs to choose at each round of play one of K arms, each characterized by an unknown reward distribution. Reward realizations are only observed when an arm is selected, and the gambler's objective is to maximize his cumulative expected earnings over some given horizon of play T. To do this, the gambler needs to acquire information about arms (exploration) while simultaneously optimizing immediate rewards (exploitation); the price paid due to this trade off is often referred to as the regret, and the main question is how small can this price be as a function of the horizon length T. This problem has been studied extensively when the reward distributions do not change over time; an assumption that supports a sharp characterization of the regret, yet is often violated in practical settings. In this paper, we focus on a MAB formulation which allows for a broad range of temporal uncertainties in the rewards, while still maintaining mathematical tractability. We fully characterize the (regret) complexity of this class of MAB problems by establishing a direct link between the extent of allowable reward "variation" and the minimal achievable regret, and by establishing a connection between the adversarial and the stochastic MAB frameworks.

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Stochastic Multi-Armed-Bandit Problem with Non-stationary Rewards

This paper investigates the potential for extreme co-movements between financial assets by directly testing the underlying dependence structure. In particular, a t-dependence structure, derived from the Student t-distribution, is used as a proxy to test for this extremal behavior. Tests in three different markets (equities, currencies, and commodities) indicate that extreme co-movements are statistically significant. Moreover, the "correlation-based" Gaussian dependence structure, underlying the multivariate Normal distribution, is rejected with negligible error probability when tested against the t-dependence alternative. The economic significance of these results is illustrated via three examples: co-movements across the G5 equity markets; portfolio value-at-risk calculations; and, pricing credit derivatives. This paper investigates the potential for extreme co-movements between financial assets by directly testing the underlying dependence structure. In particular, a t-dependence structure, derived from the Student t-distribution, is used as a proxy to test for this extremal behavior. Using likelihood ratio-based methods, we show that the presence of extreme co-movements is statistically significant in three asset markets (equities, currencies, and commodities), as well as across international (G5) equity markets. In addition, this likelihood ratio test indicates that the "correlation-based" Gaussian dependence structure is not supported on the basis of observed asset co-movements. The economic significance and consequences of these results are illustrated via several examples.

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Beyond Correlation: Extreme Co-movements Between Financial Assets

We investigate the security of quantum key distribution with entangled photons, focusing on the two-photon variation of the Bennett-Brassard 1984 (BB84) protocol proposed in 1992 by Bennett, Brasard, and Mermin (BBM92). We present a proof of security which applies to realistic sources, and to untrustable sources which can be placed outside the labs of the two receivers. The proof is restricted to individual eavesdropping attacks, and assumes that the detection apparatus is trustable. We find that the average collision probability for the BBM92 protocol is the same as that of the BB84 protocol with an ideal single-photon source. This indicates that there is no analog in BBM92 to photon splitting attacks, and that the source can be placed between the two receivers without changing the form of the collision probability. We then compare the communication rate of both protocols as a function of distance, and show that BBM92 has potential for much longer communication distances, up to 170 km, in the presence of realistic experimental imperfections. Finally, we propose a scheme based on entanglement swapping that can lead to even longer distance communication. The limiting factor in this scheme is the channel loss, which imposes very slow communication rates at longer distances.

/pdf/security-of-quantum-key-distribution-with-entangled-photons-1qpbv6drfe.pdf

Assaf Zeevi

Papers

Dynamic Pricing Without Knowing the Demand Function: Risk Bounds and Near-Optimal Algorithms

Dynamic Pricing Without Knowing the Demand Function: Risk Bounds and Near-Optimal Algorithms

Stochastic Multi-Armed-Bandit Problem with Non-stationary Rewards

Beyond Correlation: Extreme Co-movements Between Financial Assets

Security of quantum key distribution with entangled photons against individual attacks