Econometrics: Mathematical Methods & Programming eJournal最新文献_第3页

Middle Class as a Stabilized Dynamic System in Economy 中产阶级作为经济稳定的动力系统

Econometrics: Mathematical Methods & Programming eJournal Pub Date : 2020-04-26 DOI: 10.2139/ssrn.3585683

D. Semyonov

引用次数: 0

A Stochastic LQR Model for Child Order Placement in Algorithmic Trading 算法交易中子订单的随机LQR模型

Econometrics: Mathematical Methods & Programming eJournal Pub Date : 2020-03-25 DOI: 10.2139/ssrn.3574365

Jackie Shen

{"title":"A Stochastic LQR Model for Child Order Placement in Algorithmic Trading","authors":"Jackie Shen","doi":"10.2139/ssrn.3574365","DOIUrl":"https://doi.org/10.2139/ssrn.3574365","url":null,"abstract":"Modern Algorithmic Trading (\"Algo\") allows institutional investors and traders to liquidate or establish big security positions in a fully automated or low-touch manner. Most existing academic or industrial Algos focus on how to \"slice\" a big parent order into smaller child orders over a given time horizon. Few models rigorously tackle the actual placement of these child orders. Instead, placement is mostly done with a combination of empirical signals and heuristic decision processes. A self-contained, realistic, and fully functional Child Order Placement (COP) model may never exist due to all the inherent complexities, e.g., fragmentation due to multiple venues, dynamics of limit order books, lit vs. dark liquidity, different trading sessions and rules. In this paper, we propose a reductionism COP model that focuses exclusively on the interplay between placing passive limit orders and sniping using aggressive takeout orders. The dynamic programming model assumes the form of a stochastic linear-quadratic regulator (LQR) and allows closed-form solutions under the backward Bellman equations. Explored in detail are model assumptions and general settings, the choice of state and control variables and the cost functions, and the derivation of the closed-form solutions.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"81 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131484367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Double Machine Learning Based Program Evaluation under Unconfoundedness 基于双机器学习的无混杂程序评价

Econometrics: Mathematical Methods & Programming eJournal Pub Date : 2020-03-06 DOI: 10.1093/ectj/utac015

M. Knaus

引用次数: 36

Managing Electric Vehicle Charging: An Exponential Cone Programming Approach 电动汽车充电管理:一个指数锥规划方法

Econometrics: Mathematical Methods & Programming eJournal Pub Date : 2020-03-03 DOI: 10.2139/ssrn.3548028

Li Chen, Long He, Y. Zhou

{"title":"Managing Electric Vehicle Charging: An Exponential Cone Programming Approach","authors":"Li Chen, Long He, Y. Zhou","doi":"10.2139/ssrn.3548028","DOIUrl":"https://doi.org/10.2139/ssrn.3548028","url":null,"abstract":"A key to the mass adoption of electric vehicles (EVs) is ease of charging, in which public charging will play an increasingly important role. We study the EV charging management of a charging service provider, which faces uncertainty in customer arrivals (e.g., arrival/departure time and charging requirements) and a tariff structure including demand charges (costs related to the highest per-period charging quantity in a finite horizon). We formulate this problem to minimize the total expected costs as a two-stage stochastic program. A common approach to solve this program, sample average approximation, suffers from its large-scale nature. Therefore, we develop an approach based on exponential cone programs, ECP-U and ECP-C for the uncapacitated and capacitated cases, respectively, which can be solved efficiently. We obtain ECP-U by leveraging the problem structure and also provide a theoretical performance guarantee. We obtain ECP-C by also using the idea from distributionally robust optimization to employ an entropic dominance ambiguity set. Based on numerical experiments with a model calibrated to EV charging data from the U.K., we demonstrate that ECP-C not only runs faster than sample average approximation (about sixty times faster for a representative capacity level) but also leads to a lower out-of-sample expected cost and the standard deviation of this cost. Our numerical results also shed light on the effect of the composition of demand charges in smoothing electricity load over time. Our methods to construct both ECP approximations could potentially be used to solve other two-stage stochastic linear programs.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-03-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128288456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Quantum Electrodynamics (QED) Renormalization is a Logical Paradox, Zeta Function Regularization is Logically Invalid, and Both are Mathematically Invalid 量子电动力学(QED)重整化是一个逻辑悖论，Zeta函数正则化是逻辑无效的，两者在数学上都是无效的

Econometrics: Mathematical Methods & Programming eJournal Pub Date : 2020-01-09 DOI: 10.2139/ssrn.3516530

Ayal Sharon

{"title":"Quantum Electrodynamics (QED) Renormalization is a Logical Paradox, Zeta Function Regularization is Logically Invalid, and Both are Mathematically Invalid","authors":"Ayal Sharon","doi":"10.2139/ssrn.3516530","DOIUrl":"https://doi.org/10.2139/ssrn.3516530","url":null,"abstract":"Quantum Electrodynamics (QED) renormalizaion is a paradox. It uses the Euler-Mascheroni constant, which is defined by a conditionally convergent series. But Riemann's series theorem proves that any conditionally convergent series can be rearranged to be divergent. This contradiction (a series that is both convergent and divergent) is a paradox in \"classical\" logic, intuitionistic logic, and Zermelo-Fraenkel set theory, and also contradicts the commutative and associative properties of addition. Therefore QED is mathematically invalid. Zeta function regularization equates two definitions of the Zeta function at domain values where they contradict (where the Dirichlet series definition is divergent and Riemann's definition is convergent). Doing so either creates a paradox (if Riemann's definition is true), or is logically invalid (if Riemann's definition is false). We show that Riemann's definition is false, because the derivation of Riemann's definition includes a contradiction: the use of both the Hankel contour and Cauchy's integral theorem. Also, a third definition of the Zeta function is proven to be false. The Zeta function has no zeros, so the Riemann hypothesis is a paradox, due to material implication and \"vacuous subjects\".","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"185 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115515007","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A New Set of Stability Criteria Extending Lyapunov's Direct Method 推广Lyapunov直接法的一组新的稳定性判据

Econometrics: Mathematical Methods & Programming eJournal Pub Date : 2020-01-07 DOI: 10.2139/ssrn.3516858

W. Li

{"title":"A New Set of Stability Criteria Extending Lyapunov's Direct Method","authors":"W. Li","doi":"10.2139/ssrn.3516858","DOIUrl":"https://doi.org/10.2139/ssrn.3516858","url":null,"abstract":"A dynamical system is a mathematical model described by a high dimensional ordinary differential equation for a wide variety of real world phenomena, which can be as simple as a clock pendulum or as complex as a chaotic Lorenz system. Stability is an important topic in the studies of the dynamical system. A major challenge is that the analytical solution of a time-varying nonlinear dynamical system is in general not known. Lyapunov's direct method is a classical approach used for many decades to study stability without explicitly solving the dynamical system, and has been successfully employed in numerous applications ranging from aerospace guidance systems, chaos theory, to traffic assignment. Roughly speaking, an equilibrium is stable if an energy function monotonically decreases along the trajectory of the dynamical system. This paper extends Lyapunov's direct method by allowing the energy function to follow a rich set of dynamics. More precisely, the paper proves two theorems, one on globally uniformly asymptotic stability and the other on stability in the sense of Lyapunov, where stability is guaranteed provided that the evolution of the energy function satisfies an inequality of a non-negative Hurwitz polynomial differential operator, which uses not only the first-order but also high-order time derivatives of the energy function. The classical Lyapunov theorems are special cases of the extended theorems. the paper provides an example in which the new theorem successfully determines stability while the classical Lyapunov's direct method fails.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131245540","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Comparison Study and Operation Collapsing Issues for Serial Implementation of Square Matrix Multiplication Approach Suitable in High Performance Computing Environment 适用于高性能计算环境的方阵乘法串行实现的比较研究及运算崩溃问题

Econometrics: Mathematical Methods & Programming eJournal Pub Date : 2020-01-01 DOI: 10.2139/ssrn.3585762

S. Chatterjee

{"title":"Comparison Study and Operation Collapsing Issues for Serial Implementation of Square Matrix Multiplication Approach Suitable in High Performance Computing Environment","authors":"S. Chatterjee","doi":"10.2139/ssrn.3585762","DOIUrl":"https://doi.org/10.2139/ssrn.3585762","url":null,"abstract":"Multiplication between two square matrices is one of the fundamental computational approach in the domain of mathematics and computer science where it is fully recognized as a fore most technique for several interdisciplinary domain and sub domains like linear algebra, graph theory, multidimensional graphics, cryptographic computation, convolution neural network, deep learning, digital signal processing, medical image processing, steganography, relativity theory, quantum computing and many others. In a high-performance computing environment computational complexity analysis of matrix multiplication algorithm ensures a powerful paradox that takes a massive data processing approach to the world where problem solution feasibility comes down in respect of operation and time. In our paper we have analyze different methods to multiply two square matrices (like 2×2 matrices) and their arithmetic complexity analysis in a asymptotic flavor along with operation collapsing issues through serial processing technique. We have analytically and experimentally explained and shown using MATLAB 9.3 simulator that fast matrix multiplication approach like Strassen and Winograd perform much better than conventional matrix multiplication algorithm especially for large amount of data.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129992398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The Stability of MNL-Based Demand under Dynamic Customer Substitution and its Algorithmic Implications 动态客户替代下基于mnl的需求稳定性及其算法启示

Econometrics: Mathematical Methods & Programming eJournal Pub Date : 2019-12-04 DOI: 10.2139/ssrn.3498325

A. Aouad, D. Segev

{"title":"The Stability of MNL-Based Demand under Dynamic Customer Substitution and its Algorithmic Implications","authors":"A. Aouad, D. Segev","doi":"10.2139/ssrn.3498325","DOIUrl":"https://doi.org/10.2139/ssrn.3498325","url":null,"abstract":"We study the dynamic assortment planning problem under the widely utilized multinomial logit choice model (MNL). In this single-period assortment optimization and inventory management problem, the retailer jointly decides on an assortment, that is, a subset of products to be offered, as well as on the inventory levels of these products, aiming to maximize the expected revenue subject to a capacity constraint on the total number of units stocked. The demand process is formed by a stochastic stream of arriving customers, who dynamically substitute between products according to the MNL model. Although this dynamic setting is extensively studied, the best known approximation algorithm guarantees an expected revenue of at least 0.139 times the optimum, assuming that the demand distribution has an increasing failure rate. In this paper, we establish novel stochastic inequalities showing that, for any given inventory level, the expected demand of each offered product is “stable” under basic algorithmic operations, such as scaling the MNL preference weights and shifting inventory across comparable products. We exploit this sensitivity analysis to devise the first approximation scheme for dynamic assortment planning under the MNL model.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132461110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 7

Optimal Dynamic Asset Allocation for DC Plan Accumulation/Decumulation: Ambition-CVAR DC计划累积/递减的最优动态资产配置:野心- cvar

Econometrics: Mathematical Methods & Programming eJournal Pub Date : 2019-11-28 DOI: 10.2139/ssrn.3495182

P. Forsyth

{"title":"Optimal Dynamic Asset Allocation for DC Plan Accumulation/Decumulation: Ambition-CVAR","authors":"P. Forsyth","doi":"10.2139/ssrn.3495182","DOIUrl":"https://doi.org/10.2139/ssrn.3495182","url":null,"abstract":"Abstract We consider the late accumulation stage, followed by the full decumulation stage, of an investor in a defined contribution (DC) pension plan. The investor’s portfolio consists of a stock index and a bond index. As a measure of risk, we use conditional value at risk (CVAR) at the end of the decumulation stage. This is a measure of the risk of depleting the DC plan, which is primarily driven by sequence of return risk and asset allocation during the decumulation stage. As a measure of reward, we use Ambition, which we define to be the probability that the terminal wealth exceeds a specified level. We develop a method for computing the optimal dynamic asset allocation strategy which generates points on the efficient Ambition-CVAR frontier. By examining the Ambition-CVAR efficient frontier, we can determine points that are Median-CVAR optimal. We carry out numerical tests comparing the Median-CVAR optimal strategy to a benchmark constant proportion strategy. For a fixed median value (from the benchmark strategy) we find that the optimal Median-CVAR control significantly improves the CVAR. In addition, the median allocation to stocks at retirement is considerably smaller than the benchmark allocation to stocks.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133406490","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 8

A Computable General Equilibrium Analysis of Brexit: Barriers to Trade and Immigration Restrictions 英国脱欧的可计算一般均衡分析:贸易壁垒和移民限制

Econometrics: Mathematical Methods & Programming eJournal Pub Date : 2019-11-25 DOI: 10.1111/twec.12881

Gabriela Ortiz Valverde, M. Latorre

{"title":"A Computable General Equilibrium Analysis of Brexit: Barriers to Trade and Immigration Restrictions","authors":"Gabriela Ortiz Valverde, M. Latorre","doi":"10.1111/twec.12881","DOIUrl":"https://doi.org/10.1111/twec.12881","url":null,"abstract":"This paper estimates the economic effects of different types of restrictions on trade and immigration in the United Kingdom after Brexit. Regarding trade restrictions, we focus on UK-EU increases of tariffs and Non-tariff barriers. We also analyse the removal of all tariffs in the UK to all its trading partners. Concerning immigration, we run a 5-year cumulative annual reduction in net migrants by 87.000 workers following OECD estimations. The study is conducted using a Computable General Equilibrium (CGE) Model, which allows us to estimate the impact on GDP, welfare, wages and capital remuneration, together with the evolution of aggregate and sectoral output, exports and imports. We obtain a more sizeable negative impact on the UK than other previous influential studies. Trade restrictions would generate welfare reductions between -0.38% and -1.94% for the UK, while they would be between -0.03% and -0.14% in the EU. This is because the EU is a crucial trade partner for the UK, which cannot be easily substituted through trade with other regions in the world. Restrictions to migrants would bring additional contractions in the range between -0.55% and -0.34% for welfare, depending on whether they affect skilled or unskilled workers, respectively.","PeriodicalId":299310,"journal":{"name":"Econometrics: Mathematical Methods & Programming eJournal","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116132342","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 17