This paper examines asymmetric and time-varying dependency structures between financial returns, using a novel approach consisting of a combination of regime-switching models and the local Gaussian correlation (LGC). We propose an LGC-based bootstrap test for whether the dependence structure in financial returns across different regimes is equal. We examine this test in a Monte Carlo study, where it shows good level and power properties. We argue that this approach is more intuitive than competing approaches, typically combining regime-switching models with copula theory. Furthermore, the LGC is a semi-parametric approach, hence avoids any parametric specification of the dependence structure. We illustrate our approach using returns from the US-UK stock markets and the US stock and government bond markets. Using a two-regime model for the US-UK stock returns, the test rejects equality of the dependence structure in the two regimes. Furthermore, we find evidence of lower tail dependence in the regime associated with financial downturns in the LGC structure. For a three-regime model fitted to US stock and bond returns, the test rejects equality of the dependence structures between all regime pairs. Furthermore, we find that the LGC has a primarily positive relationship in the time period 1980-2000, mostly a negative relationship from 2000 and onwards. In addition, the regime associated with bear markets indicates less, but asymmetric dependence, clearly documenting the loss of diversification benefits in times of crisis.
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This paper develops power series expansions of a general class of moment functions, including transition densities and option prices, of continuous-time Markov processes, including jump--diffusions. The proposed expansions extend the ones in Kristensen and Mele (2011) to cover general Markov processes. We demonstrate that the class of expansions nests the transition density and option price expansions developed in Yang, Chen, and Wan (2019) and Wan and Yang (2021) as special cases, thereby connecting seemingly different ideas in a unified framework. We show how the general expansion can be implemented for fully general jump--diffusion models. We provide a new theory for the validity of the expansions which shows that series expansions are not guaranteed to converge as more terms are added in general. Thus, these methods should be used with caution. At the same time, the numerical studies in this paper demonstrate good performance of the proposed implementation in practice when a small number of terms are included.
This paper is dedicated to the mathematical analysis of finite difference schemes for the angular diffusion operator present in the azimuth-independent Fokker-Planck equation. The study elucidates the reasons behind the lack of convergence in half range mode for certain widely recognized discrete ordinates methods, and establishes sets of sufficient conditions to ensure that the schemes achieve convergence of order $2$. In the process, interesting properties regarding Gaussian nodes and weights, which until now have remained unnoticed by mathematicians, naturally emerge.
Graph data management is instrumental for several use cases such as recommendation, root cause analysis, financial fraud detection, and enterprise knowledge representation. Efficiently supporting these use cases yields a number of unique requirements, including the need for a concise query language and graph-aware query optimization techniques. The goal of the Linked Data Benchmark Council (LDBC) is to design a set of standard benchmarks that capture representative categories of graph data management problems, making the performance of systems comparable and facilitating competition among vendors. LDBC also conducts research on graph schemas and graph query languages. This paper introduces the LDBC organization and its work over the last decade.
This paper focuses on investigating the density convergence of a fully discrete finite difference method when applied to numerically solve the stochastic Cahn--Hilliard equation driven by multiplicative space-time white noises. The main difficulty lies in the control of the drift coefficient that is neither globally Lipschitz nor one-sided Lipschitz. To handle this difficulty, we propose a novel localization argument and derive the strong convergence rate of the numerical solution to estimate the total variation distance between the exact and numerical solutions. This along with the existence of the density of the numerical solution finally yields the convergence of density in $L^1(\mathbb{R})$ of the numerical solution. Our results partially answer positively to the open problem emerged in [J. Cui and J. Hong, J. Differential Equations (2020)] on computing the density of the exact solution numerically.
E-commerce, a type of trading that occurs at a high frequency on the Internet, requires guaranteeing the integrity, authentication and non-repudiation of messages through long distance. As current e-commerce schemes are vulnerable to computational attacks, quantum cryptography, ensuring information-theoretic security against adversary's repudiation and forgery, provides a solution to this problem. However, quantum solutions generally have much lower performance compared to classical ones. Besides, when considering imperfect devices, the performance of quantum schemes exhibits a significant decline. Here, for the first time, we demonstrate the whole e-commerce process of involving the signing of a contract and payment among three parties by proposing a quantum e-commerce scheme, which shows resistance of attacks from imperfect devices. Results show that with a maximum attenuation of 25 dB among participants, our scheme can achieve a signature rate of 0.82 times per second for an agreement size of approximately 0.428 megabit. This proposed scheme presents a promising solution for providing information-theoretic security for e-commerce.
This paper studies the fusogenicity of cationic liposomes in relation to their surface distribution of cationic lipids and utilizes membrane phase separation to control this surface distribution. It is found that concentrating the cationic lipids into small surface patches on liposomes, through phase-separation, can enhance liposome's fusogenicity. Further concentrating these lipids into smaller patches on the surface of liposomes led to an increased level of fusogenicity. These experimental findings are supported by numerical simulations using a mathematical model for phase-separated charged liposomes. Findings of this study may be used for design and development of highly fusogenic liposomes with minimal level of toxicity.
We propose a generalization of nonlinear stability of numerical one-step integrators to Riemannian manifolds in the spirit of Butcher's notion of B-stability. Taking inspiration from Simpson-Porco and Bullo, we introduce non-expansive systems on such manifolds and define B-stability of integrators. In this first exposition, we provide concrete results for a geodesic version of the Implicit Euler (GIE) scheme. We prove that the GIE method is B-stable on Riemannian manifolds with non-positive sectional curvature. We show through numerical examples that the GIE method is expansive when applied to a certain non-expansive vector field on the 2-sphere, and that the GIE method does not necessarily possess a unique solution for large enough step sizes. Finally, we derive a new improved global error estimate for general Lie group integrators.
This paper derives a discrete dual problem for a prototypical hybrid high-order method for convex minimization problems. The discrete primal and dual problem satisfy a weak convex duality that leads to a priori error estimates with convergence rates under additional smoothness assumptions. This duality holds for general polytopal meshes and arbitrary polynomial degree of the discretization. A nouvelle postprocessing is proposed and allows for a~posteriori error estimates on simplicial meshes using primal-dual techniques. This motivates an adaptive mesh-refining algorithm, which performs superiorly compared to uniform mesh refinements.
Confidence intervals based on the central limit theorem (CLT) are a cornerstone of classical statistics. Despite being only asymptotically valid, they are ubiquitous because they permit statistical inference under very weak assumptions, and can often be applied to problems even when nonasymptotic inference is impossible. This paper introduces time-uniform analogues of such asymptotic confidence intervals. To elaborate, our methods take the form of confidence sequences (CS) -- sequences of confidence intervals that are uniformly valid over time. CSs provide valid inference at arbitrary stopping times, incurring no penalties for "peeking" at the data, unlike classical confidence intervals which require the sample size to be fixed in advance. Existing CSs in the literature are nonasymptotic, and hence do not enjoy the aforementioned broad applicability of asymptotic confidence intervals. Our work bridges the gap by giving a definition for "asymptotic CSs", and deriving a universal asymptotic CS that requires only weak CLT-like assumptions. While the CLT approximates the distribution of a sample average by that of a Gaussian at a fixed sample size, we use strong invariance principles (stemming from the seminal 1960s work of Strassen and improvements by Koml\'os, Major, and Tusn\'ady) to uniformly approximate the entire sample average process by an implicit Gaussian process. As an illustration of our theory, we derive asymptotic CSs for the average treatment effect using efficient estimators in observational studies (for which no nonasymptotic bounds can exist even in the fixed-time regime) as well as randomized experiments, enabling causal inference that can be continuously monitored and adaptively stopped.
In this paper we develop a novel neural network model for predicting implied volatility surface. Prior financial domain knowledge is taken into account. A new activation function that incorporates volatility smile is proposed, which is used for the hidden nodes that process the underlying asset price. In addition, financial conditions, such as the absence of arbitrage, the boundaries and the asymptotic slope, are embedded into the loss function. This is one of the very first studies which discuss a methodological framework that incorporates prior financial domain knowledge into neural network architecture design and model training. The proposed model outperforms the benchmarked models with the option data on the S&P 500 index over 20 years. More importantly, the domain knowledge is satisfied empirically, showing the model is consistent with the existing financial theories and conditions related to implied volatility surface.
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