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Trade execution games in a Markovian environment

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arXiv 2024年

作者： Ohnishi, Masamitsu Shimoshimizu, Makoto Faculty of Informatics Yamato University Osaka Suita City564-0082 Japan Center for Mathematical Modeling and Data Science Osaka University Toyonaka City Osaka560-8531 Japan Department of Industrial and Systems Engineering Tokyo University of Science 2641 Yamazaki Noda City Chiba278-8510 Japan

This paper examines a trade execution game for two large traders in a generalized price impact model. We incorporate a stochastic and sequentially dependent factor that exogenously affects the market price into financial markets. Our model accounts for how strategic and environmental uncertainties affect the large traders' execution strategies. We formulate an expected utility maximization problem for two large traders as a Markov game model. Applying the backward induction method of dynamic programming, we provide an explicit closed-form execution strategy at a Markov perfect equilibrium. Our theoretical results reveal that the execution strategy generally lies in a dynamic and non-randomized class;it becomes deterministic if the Markovian environment is also deterministic. In addition, our simulation-based numerical experiments suggest that the execution strategy captures various features observed in financial markets. Copyright © 2024, The Authors. All rights reserved.

关键词： Dynamic programming

An Orthogonal Polynomial Kernel-Based Machine Learning Model for Differential-Algebraic Equations

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arXiv 2024年

作者： Taheri, Tayebeh Aghaei, Alireza Afzal Parand, Kourosh Department of Computer and Data Sciences Faculty of Mathematical Sciences Shahid Beheshti University Tehran Iran Department of Cognitive Modeling Institute for Cognitive and Brain Sciences Shahid Beheshti University Tehran Iran Department of Statistics and Actuarial Science University of Waterloo Waterloo Canada

The recent introduction of the Least-Squares Support Vector Regression (LS-SVR) algorithm for solving differential and integral equations has sparked interest. In this study, we expand the application of this algorithm to address systems of differential-algebraic equations (DAEs). Our work presents a novel approach to solving general DAEs in an operator format by establishing connections between the LS-SVR machine learning model, weighted residual methods, and Legendre orthogonal polynomials. To assess the effectiveness of our proposed method, we conduct simulations involving various DAE scenarios, such as nonlinear systems, fractional-order derivatives, integro-differential, and partial DAEs. Finally, we carry out comparisons between our proposed method and currently established state-of-the-art approaches, demonstrating its reliability and effectiveness. © 2024, CC BY.

关键词： Integral equations

Quick estimation of parameters for the land surface data assimilation system and its influence based on the extended Kalman filter and automatic differentiation

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science China Earth sciences 2023年第11期66卷 2546-2562页

作者： Jiaxin TIAN Hui LU Kun YANG Jun QIN Long ZHAO Jianhong ZHOU Yaozhi JIANG Xiaogang MA Department of Earth System Science Ministry of Education Key Laboratory for Earth System ModelingInstitute for Global Change StudiesTsinghua UniversityBeijing 100084China National Tibetan Plateau Data Center Key Laboratory of Tibetan Environmental Changes and Land Surfaces ProcessesInstitute of Tibetan Plateau ResearchChinese Academy of SciencesBeijing 100101China State Key Laboratory of Resources and Environmental Information System Institute of Geographic Sciences and Natural Resources ResearchChinese Academy of SciencesBeijing 100101China Chongqing Jinfo Mountain Karst Ecosystem National Observation and Research Station School of Geographical SciencesSouth-west UniversityChongqing 400715China Tsinghua University(Department of Earth System Science)-Xi’an Institute of Surveying and Mapping Joint Research Center for Next-Generation Smart Mapping Beijing 100084China

Soil moisture plays a crucial role in drought monitoring,flood forecasting,and water resource *** assimilation methods can integrate the strengths of land surface models(LSM)and remote sensing data to generate highprecision and spatio-temporally continuous soil moisture ***,one of the challenges of the land data assimilation system(LDAS)is how to accurately estimate model and observation *** address this,we had previously proposed a dualcycle assimilation algorithm that can simultaneously estimate the model and observation errors,LSM parameters,and observation operator ***,this algorithm requires a large ensemble size to guarantee stable parameter estimates,resulting in low efficiency and limiting its large-scale *** address this limitation,the authors employed the following approaches:(1)using automatic differentiation to compute the Jacobian matrix of LSM instead of constructing a tangent linear model of LSM,and(2)replacing the ensemble Kalman filter framework with the extended Kalman filter(EKF)framework to improve the efficiency of parameter optimization for the dual-cycle *** EKF-based dual-cycle algorithm accelerated the parameter estimation efficiency near 60 times during a 90-day time period with a model integration time step of 1 *** evaluate the dual-cycle LDAS at the regional-scale,it was applied to assimilate the SMAP soil moisture over the Tibetan Plateau,and soil moisture estimates were validated using in situ observations from four different climatic *** results showed that the EKF-based dual-cycle LDAS corrected biases in both the model and observations and produced more accurate estimates of soil moisture,land surface temperature,and evapotranspiration than did the open loop with default ***,the spatial distribution of soil parameters(sand content,clay content,and porosity)obtained from the LDAS was more reasonable than those of default *** EKF-based

关键词： Soil moisture data assimilation Parameter optimization Bias correction Error estimation Automatic differentiation

The horizontal magnetic primitive equations approximation of the anisotropic MHD equations in a thin 3D domain

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arXiv 2023年

作者： Zhang, Jie Liu, Wenjun School of Mathematics and Statistics Nanjing University of Information Science and Technology Nanjing210044 China Jiangsu International Joint Laboratory on System Modeling and Data Analysis Center for Applied Mathematics of Jiangsu Province Nanjing University of Information Science and Technology Nanjing210044 China

In this paper, we give a rigorous justification of the deviation of the primitive equations with only horizontal viscosity and magnetic diffusivity (PEHM) as the small aspect ratio limit of the incompressible three-dimensional scaled horizontal viscous MHD (SHMHD) equations. Choosing an aspect ratio parameter Ε ∈ (0, ∞), we consider the case that if the horizontal and vertical viscous coefficients are of µ = O(1) and ν = O(Εα), and the orders of magnetic diffusion coefficients k and σ are k = O(1) and σ = O(Εα), with α > 2, then the limiting system is the PEHM as Ε goes to zero. For H1-initial data, we prove that the global weak solutions of the SHMHD equations converge strongly to the local-in-time strong solutions of the PEHM, as Ε tends to zero. For H1-initial data with additional regularity (∂zÃ0, ∂zB˜0) ∈ Lp(Ω)(2 2-initial data, we show that the local-in-time strong solutions of the SHMHD equations converge strongly to the global-in-time strong solutions of the PEHM, as Ε goes to zero. Moreover, the rate of convergence is of the order O(Εγ/2), where γ = min{2, α − 2} with α ∈ (2, ∞). It should be noted that in contrast to the case α > 2, the case α = 2 has been investigated by Du and Li in [14], in which they consider the PEM and the rate of global-in-time convergences is of the order O(Ε).MSC Codes 35Q30, 76D03, 76D05, 35Q86, 76W05 Copyright © 2023, The Authors. All rights reserved.

关键词： Aspect ratio

Mathematical modeling and analysis of atherosclerosis based on fluid-multilayered poroelastic structure interaction model

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Research Square

Research Square 2023年

作者： An, Yanning Liu, Wenjun School of Mathematics and Statistics Nanjing University of Information Science and Technology Nanjing210044 China Jiangsu International Joint Laboratory on System Modeling and Data Analysis Center for Applied Mathematics of Jiangsu Province Nanjing University of Information Science and Technology Nanjing210044 China

In this paper, we establish a new model of atherosclerosis in the early stage based on fluid-structure interaction (FSI) model of blood vessel and prove the existence of weak solutions. The model consists of Navier-Stokes equation, Biot equations, and reaction-diffusion equations, which involves the effect of blood flow velocity on the concentration of low density lipoprotein (LDL) and other biological components. We first divide the new model into a FSI submodel and a coupled reaction-diffusion submodel, respectively. Then, by using Rothe’s method and operator splitting numerical scheme, we obtain the existence of weak solution of FSI submodel. In order to solve the nonlinear term representing the consumption of oxidized low density lipoprotein (oxLDL), we construct a regular system. The results in FSI submodel together with Schauder’s fixed point theorem allow us to obtain the existence of non-negative weak solutions for the reaction-diffusion submodel by showing the existence and non-negativity of weak solutions for the regular system. © 2023, CC BY.

关键词： Navier Stokes equations

Combining experimental and historical data for policy evaluation 24

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Combining experimental and historical data for policy evalua...

Proceedings of the 41st International Conference on Machine Learning

作者： Ting Li Chengchun Shi Qianglin Wen Yang Sui Yongli Qin Chunbo Lai Hongtu Zhu School of Statistics and Management Shanghai University of Finance and Economics Department of Statistics London School of Economics and Political Science Yunnan Key Laboratory of Statistical Modeling and Data Analysis Yunnan University Didi Chuxing Department of Biostatistics The University of North Carolina at Chapel Hill

This paper studies policy evaluation with multiple data sources, especially in scenarios that involve one experimental dataset with two arms, complemented by a historical dataset generated under a single control arm. We propose novel data integration methods that linearly integrate base policy value estimators constructed based on the experimental and historical data, with weights optimized to minimize the mean square error (MSE) of the resulting combined estimator. We further apply the pessimistic principle to obtain more robust estimators, and extend these developments to sequential decision making. Theoretically, we establish non-asymptotic error bounds for the MSEs of our proposed estimators, and derive their oracle, efficiency and robustness properties across a broad spectrum of reward shift scenarios. Numerical experiments and real-data-based analyses from a ridesharing company demonstrate the superior performance of the proposed estimators.

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Continuous data assimilation for the three dimensional primitive equations with magnetic field

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arXiv 2023年

作者： Zhao, Yongqing Liu, Wenjun Lv, Guangying Wang, Yuepeng School of Mathematics and Statistics Nanjing University of Information Science and Technology Nanjing210044 China Jiangsu International Joint Laboratory on System Modeling and Data Analysis Center for Applied Mathematics of Jiangsu Province Nanjing University of Information Science and Technology Nanjing210044 China

In this paper, the problem of continuous data assimilation of three dimensional primitive equations with magnetic field in thin domain is studied. We establish the well-posedness of the assimilation system and prove that the H2-strong solution of the assimilation system converges exponentially to the reference solution in the sense of L2 as t → ∞. We also study the sensitivity analysis of the assimilation system and prove that a sequence of solutions of the difference quotient equation converge to the unique solution of the formal sensitivity *** Codes 35Q35, 34D06, 37C50 Copyright © 2023, The Authors. All rights reserved.

关键词： Sensitivity analysis

A UNIFYING FRAMEWORK FOR INTERPOLATORY L2-OPTIMAL REDUCED-ORDER modeling

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arXiv 2022年

作者： Mlinarić, Petar Gugercin, Serkan Department of Mathematics Virginia Tech BlacksburgVA24061 United States Department of Mathematics Division of Computational Modeling and Data Analytics Academy of Data Science Virginia Tech BlacksburgVA24061 United States

We develop a unifying framework for interpolatory L2-optimal reduced-order modeling for a wide classes of problems ranging from stationary models to parametric dynamical systems. We first show that the framework naturally covers the well-known interpolatory necessary conditions for H2-optimal model order reduction and leads to the interpolatory conditions for H2 ⨂ L2-optimal model order reduction of multi-input/multi-output parametric dynamical systems. Moreover, we derive novel interpolatory optimality conditions for rational discrete least-squares minimization and for L2-optimal model order reduction of a class of parametric stationary models. We show that bitangential Hermite interpolation appears as the main tool for optimality across different domains. The theoretical results are illustrated on two numerical examples. Copyright © 2022, The Authors. All rights reserved.

关键词： Linear time-invariant system

Inference on high-dimensional single-index models with streaming data

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The Journal of Machine Learning Research

The Journal of Machine Learning Research 2024年第1期25卷 16489-16556页

作者： Dongxiao Han Jinhan Xie Jin Liu Liuquan Sun Jian Huang Bei Jiang Linglong Kong School of Statistics and Data Science KLMDASR LEBPS and LPMC Nankai University Tianjin China Yunnan Key Laboratory of Statistical Modeling and Data Analysis Yunnan University Kunming China and Department of Mathematical and Statistical Sciences University of Alberta Edmonton AB Canada Academy of Mathematics and Systems Science Chinese Academy of Sciences and School of Mathematical Sciences University of Chinese Academy of Sciences Beijing China Department of Applied Mathematics The Hong Kong Polytechnic University Hong Kong China Department of Mathematical and Statistical Sciences University of Alberta Edmonton AB Canada

Traditional statistical methods are faced with new challenges due to streaming data. The major challenge is the rapidly growing volume and velocity of data, which makes storing such huge data sets in memory impossible. The paper presents an online inference framework for regression parameters in high-dimensional semiparametric single-index models with unknown link functions. The proposed online procedure updates only the current data batch and summary statistics of historical data instead of re-accessing the entire raw data set. At the same time, we do not need to estimate the unknown link function, which is a highly challenging task. In addition, a generalized convex loss function is used in the proposed inference procedure. To illustrate the proposed method, we use the Huber loss function and the negative log-likelihood of the logistic regression model. In this study, the asymptotic normality of the proposed online debiased Lasso estimators and the bounds of the proposed online Lasso estimators are investigated. To evaluate the performance of the proposed method, extensive simulation studies have been conducted. We provide applications to Nasdaq stock prices and financial distress data sets.

关键词： high-dimensional data lasso single-index models statistical inference streaming data