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A New Lagrangean Approach for the Travelling Salesman Problem 旅行商问题的一种新的拉格朗日方法
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2015-01-19 DOI: 10.2139/ssrn.2551758
K. Jørnsten, J. Kalcsics
{"title":"A New Lagrangean Approach for the Travelling Salesman Problem","authors":"K. Jørnsten, J. Kalcsics","doi":"10.2139/ssrn.2551758","DOIUrl":"https://doi.org/10.2139/ssrn.2551758","url":null,"abstract":"In this paper, we use a reformulation of the symmetric and the asymmetric travelling salesman problem more suitable for Lagrangean relaxation and analyse the new approach on examples from TSP Lib. Furthermore the Lagrangean relaxed subproblems are travelling salesman alike which means that almost all that is known on the travelling salesman polytope can be used when the subproblems are to be solved.","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114326179","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
A Solvable Two-Dimensional Degenerate Singular Stochastic Control Problem with Non Convex Costs 具有非凸代价的二维退化奇异随机控制问题
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2014-11-10 DOI: 10.2139/ssrn.2533999
T. Angelis, Giorgio Ferrari, J. Moriarty
{"title":"A Solvable Two-Dimensional Degenerate Singular Stochastic Control Problem with Non Convex Costs","authors":"T. Angelis, Giorgio Ferrari, J. Moriarty","doi":"10.2139/ssrn.2533999","DOIUrl":"https://doi.org/10.2139/ssrn.2533999","url":null,"abstract":"In this paper we provide a complete theoretical analysis of a two-dimensional degenerate non convex singular stochastic control problem. The optimisation is motivated by a storage-consumption model in an electricity market, and features a stochastic real-valued spot price modelled by Brownian motion. We find analytical expressions for the value function, the optimal control and the boundaries of the action and inaction regions. The optimal policy is characterised in terms of two monotone and discontinuous repelling free boundaries, although part of one boundary is constant and and the smooth fit condition holds there.","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"30 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121604389","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: 11
Kernel Density Estimation with Ripley's Circumferential Correction 基于Ripley周向校正的核密度估计
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2014-10-25 DOI: 10.2139/ssrn.2514890
Arthur Charpentier, E. Gallic
{"title":"Kernel Density Estimation with Ripley's Circumferential Correction","authors":"Arthur Charpentier, E. Gallic","doi":"10.2139/ssrn.2514890","DOIUrl":"https://doi.org/10.2139/ssrn.2514890","url":null,"abstract":"In this paper, we investigate (and extend) Ripley's circumference method to correct bias of density estimation of edges (or frontiers) of regions. The idea of the method was theoretical and difficult to implement. We provide a simple technique - based of properties of Gaussian kernels - to efficiently compute weights to correct border bias on frontiers of the region of interest, with an automatic selection of an optimal radius for the method. We illustrate the use of that technique to visualize hot spots of car accidents and campsite locations, as well as location of bike thefts.","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"143 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121658779","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
Numerical Algorithms for Research and Development Stochastic Control Models 研究与开发随机控制模型的数值算法
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2014-09-30 DOI: 10.21314/JCF.2014.282
C. Leung, Y. Kwok
{"title":"Numerical Algorithms for Research and Development Stochastic Control Models","authors":"C. Leung, Y. Kwok","doi":"10.21314/JCF.2014.282","DOIUrl":"https://doi.org/10.21314/JCF.2014.282","url":null,"abstract":"We consider the optimal strategy of research and development (R&D) expenditure adopted by a firm that engages in R&D to develop an innovative product to be launched in the market. The firm faces technological uncertainty associated with the success of the R&D effort and market uncertainty about the stochastic revenue flow generated by the new product. Our model departs from most R&D models by assuming that the firm’s knowledge accumulation has an impact on the R&D process, so the hazard rate of arrival of R&D success is no longer memoryless. Also, we assume a finite life span of the technologies that the product depends on. In this paper, we propose efficient finite difference schemes that solve the Hamilton–Jacobi–Bellman formulation of the resulting finite time R&D stochastic control models with an optimal control on R&D expenditure and an optimal stopping rule on the abandonment of R&D effort. The optimal strategies of R&D expenditure with varying sets of model parameters are analyzed. In particular, we observe that R&D expenditure decreases with a firm’s knowledge stock and may even drop to zero when the accumulation level is sufficiently high.","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128507042","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
Non-Implementability of Arrow-Debreu Equilibria by Continuous Trading under Knightian Uncertainty knight不确定性下连续交易的Arrow-Debreu均衡的不可实现性
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2014-09-18 DOI: 10.2139/ssrn.2500793
F. Riedel, Patrick Beissner
{"title":"Non-Implementability of Arrow-Debreu Equilibria by Continuous Trading under Knightian Uncertainty","authors":"F. Riedel, Patrick Beissner","doi":"10.2139/ssrn.2500793","DOIUrl":"https://doi.org/10.2139/ssrn.2500793","url":null,"abstract":"Under risk, Arrow-Debreu equilibria can be implemented as Radner equilibria by continuous trading of few long-lived securities. We show that this result generically fails if there is Knightian uncertainty in the volatility. Implementation is only possible if all discounted net trades of the equilibrium allocation are mean ambiguity-free.","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"96 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115315368","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
Dynamic CRRA-Utility Indifference Value in Generalized Cox Model 广义Cox模型的动态crra -效用无差异值
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2014-09-04 DOI: 10.2139/ssrn.2491412
Kun Tian, Dewen Xiong, Z. Ye
{"title":"Dynamic CRRA-Utility Indifference Value in Generalized Cox Model","authors":"Kun Tian, Dewen Xiong, Z. Ye","doi":"10.2139/ssrn.2491412","DOIUrl":"https://doi.org/10.2139/ssrn.2491412","url":null,"abstract":"We assume that there exist two kinds of investors in the market, the 𝔽-investors and the 𝔾-investors. The 𝔽-investors have the market information 𝔽, which is given by a d-dimensional Brownian motion W = (W1,...;Wd)' as well as an integer-valued random measure μ(du, dy). The market might default at time ˜τ, modeled by the so called the generalized Cox model, and the information of the 𝔾-investors is the by the default, progressively enlarged fitration of 𝔽. We give the explicit form of the survival process. Then we derive the dynamic CRRA-utility indifference value(UIV) Ct of the 𝔽-investors with respect to the 𝔾-investors and describe the dynamics of Ct by two BSDEs. In the end, we give an example in which we can give the explicit expression of Ct. For the generalized Cox model we typically have that Ct ≥ 1 in contrast to the standard Cox model.","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"205 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134554988","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
Some Mathematical Properties of the Dynamically Inconsistent Bellman Equation: A Note on the Two-sided Altruism Dynamics 动态不一致Bellman方程的一些数学性质——关于双边利他主义动力学的注解
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2014-09-01 DOI: 10.2139/ssrn.2231847
Takaaki Aoki
{"title":"Some Mathematical Properties of the Dynamically Inconsistent Bellman Equation: A Note on the Two-sided Altruism Dynamics","authors":"Takaaki Aoki","doi":"10.2139/ssrn.2231847","DOIUrl":"https://doi.org/10.2139/ssrn.2231847","url":null,"abstract":"This article describes some dynamic aspects on dynastic utility incorporating two-sided altruism with an OLG setting. We analyzed the special case where the weights of two-sided altruism are dynamically inconsistent. The Bellman equation for two-sided altruism proves to be reduced to one-sided dynamic problem, but the effective discount factor is different only in the current generation. We show that a contraction mapping result of value function cannot be achieved in general, and that there can locally exist an infinite number of self-consistent policy functions with distinct steady states (indeterminacy of self-consistent policy functions).","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115229014","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
Unanticipated Features of the Multidimensional G-Normal Distribution 多维g -正态分布的意外特征
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2014-07-18 DOI: 10.2139/ssrn.2468364
Erhan Bayraktar, A. Munk
{"title":"Unanticipated Features of the Multidimensional G-Normal Distribution","authors":"Erhan Bayraktar, A. Munk","doi":"10.2139/ssrn.2468364","DOIUrl":"https://doi.org/10.2139/ssrn.2468364","url":null,"abstract":"In one dimension, the theory of the G-normal distribution is well-developed, and many results from the classical setting have a nonlinear counterpart. Significant challenges remain in multiple dimensions, and some of what has already been discovered is quite nonintuitive. By answering several classically-inspired questions concerning independence, covariance uncertainty, and behavior under certain linear operations, we continue to highlight the fascinating range of unexpected attributes of the multidimensional G-normal distribution.","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132400884","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
Semiclassical Approximation in Stochastic Optimal Control: I. Portfolio Construction Problem 随机最优控制中的半经典逼近:1 .投资组合构造问题
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2014-06-22 DOI: 10.2139/ssrn.2457664
S. Chaiworawitkul, P. Hagan, Andrew S. Lesniewski
{"title":"Semiclassical Approximation in Stochastic Optimal Control: I. Portfolio Construction Problem","authors":"S. Chaiworawitkul, P. Hagan, Andrew S. Lesniewski","doi":"10.2139/ssrn.2457664","DOIUrl":"https://doi.org/10.2139/ssrn.2457664","url":null,"abstract":"This is the first in a series of papers in which we study an efficient approximation scheme for solving the Hamilton-Jacobi-Bellman equation for multi-dimensional problems in stochastic control theory. The method is a combination of a WKB style asymptotic expansion of the value function, which reduces the second order HJB partial differential equation to a hierarchy of first order PDEs, followed by a numerical algorithm to solve the first few of the resulting first order PDEs. This method is applicable to stochastic systems with a relatively large number of degrees of freedom, and does not seem to suffer from the curse of dimensionality. Computer code implementation of the method using modest computational resources runs essentially in real time. We apply the method to solve a general portfolio construction problem.","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127663040","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
A Minimax Bias Estimator for OLS Variances Under Heteroskedasticity 异方差下OLS方差的极大极小偏估计
ERN: Other Econometrics: Mathematical Methods & Programming (Topic) Pub Date : 2014-05-04 DOI: 10.2139/ssrn.2432685
Mumtaz Ahmed, A. Zaman
{"title":"A Minimax Bias Estimator for OLS Variances Under Heteroskedasticity","authors":"Mumtaz Ahmed, A. Zaman","doi":"10.2139/ssrn.2432685","DOIUrl":"https://doi.org/10.2139/ssrn.2432685","url":null,"abstract":"Analytic evaluation of heteroskedasticity consistent covariance matrix estimates (HCCME) is difficult because of the complexity of the formulae currently available. We obtain new analytic formulae for the bias of a class of estimators of the covariance matrix of OLS in a standard linear regression model. These formulae provide substantial insight into the properties and performance characteristics of these estimators. In particular, we find a new estimator which minimizes the maximum possible bias and improves substantially on the standard Eicker-White estimate.","PeriodicalId":365755,"journal":{"name":"ERN: Other Econometrics: Mathematical Methods & Programming (Topic)","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127774211","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
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