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Adaptation Bounds for Confidence Bands under Self-Similarity 自相似条件下置信带的自适应界
Mathematics eJournal Pub Date : 2018-10-23 DOI: 10.2139/ssrn.3423277
Timothy B. Armstrong
{"title":"Adaptation Bounds for Confidence Bands under Self-Similarity","authors":"Timothy B. Armstrong","doi":"10.2139/ssrn.3423277","DOIUrl":"https://doi.org/10.2139/ssrn.3423277","url":null,"abstract":"We derive bounds on the scope for a confidence band to adapt to the unknown regularity of a nonparametric function that is observed with noise, such as a regression function or density, under the self-similarity condition proposed by Gine and Nickl (2010). We find that adaptation can only be achieved up to a term that depends on the choice of the constant used to define self-similarity, and that this term becomes arbitrarily large for conservative choices of the self-similarity constant. We construct a confidence band that achieves this bound, up to a constant term that does not depend on the self-similarity constant. Our results suggest that care must be taken in choosing and interpreting the constant that defines self-similarity, since the dependence of adaptive confidence bands on this constant cannot be made to disappear asymptotically.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"23 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127810645","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: 2
Correcting Paul Samuelson’s Small Error in His November, 1963 Eulogy for Robertson: Dennis Robertson Erred Seriously in His Evaluation of Keynes’s Differential Calculus–Based Multiplier Concept in the General Theory 纠正保罗·萨缪尔森1963年11月致罗伯逊悼词中的小错误:丹尼斯·罗伯逊在《通论》中对凯恩斯基于微分法的乘数概念的评价中犯了严重错误
Mathematics eJournal Pub Date : 2018-10-13 DOI: 10.2139/ssrn.3265628
M. E. Brady
{"title":"Correcting Paul Samuelson’s Small Error in His November, 1963 Eulogy for Robertson: Dennis Robertson Erred Seriously in His Evaluation of Keynes’s Differential Calculus–Based Multiplier Concept in the General Theory","authors":"M. E. Brady","doi":"10.2139/ssrn.3265628","DOIUrl":"https://doi.org/10.2139/ssrn.3265628","url":null,"abstract":"Dennis Robertson had no understanding of how J M Keynes’s Multiplier concept was based on the use of differential calculus techniques that required one to take the mathematical limit of an infinite, decreasing, geometric series. Robertson failed to see that the derivative concept requires that one is dealing with an instantaneous rate of change. Robertson thus confused the fact that the actual multiplier process of change in the real world is not instantaneous, but requires time for the process to actually function, so that in the real world it is not instantaneous, with the mathematical theory of the multiplier. Samuelson overlooked Robertson’s very confused state of mind, resulting from his mathematical illiteracy, when he concluded that Robertson’s criticisms of Keynes’s instantaneous, theoretical multiplier concept discussions on pages 122-123 of the General Theory were sound. D. Robertson ‘s confused attempts at critiquing Keynes’s concepts of the logical theory of the multiplier and the multiplier in 1936 in his QJE article were due to his own extreme mathematical limitations, confusions and ineptness. Samuelson had recognized that this problem of mathematical illiteracy existed in the economics profession by 1936. Economists were shockingly unprepared in the use of even basic intermediate algebra.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114813815","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
Alternative Methods of Estimating the Longevity Risk 评估寿命风险的替代方法
Mathematics eJournal Pub Date : 2018-10-06 DOI: 10.2139/ssrn.3261739
Catalina Bolancé, Montserrat Guillén, A. Ornelas
{"title":"Alternative Methods of Estimating the Longevity Risk","authors":"Catalina Bolancé, Montserrat Guillén, A. Ornelas","doi":"10.2139/ssrn.3261739","DOIUrl":"https://doi.org/10.2139/ssrn.3261739","url":null,"abstract":"The aim of this paper is to estimate the longevity risk and its trend according to the age of the individual. We focus on individuals over 65. We use the value-at-risk to measure the longevity risk. We have proposed the use of an alternative methodology based on the estimation of the truncated cumulative distribution function and the quantiles. We apply a robust estimation method for fitting parametric distributions. Finally, we compare parametric and nonparametric estimations of longevity risk.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132039365","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
Information and Communication Technologies as a Didactic Tool for the Construction of Meaningful Learning in the Area of Mathematics 信息和通信技术作为数学领域建构有意义学习的教学工具
Mathematics eJournal Pub Date : 2018-10-02 DOI: 10.2139/ssrn.3639452
D. Mendoza
{"title":"Information and Communication Technologies as a Didactic Tool for the Construction of Meaningful Learning in the Area of Mathematics","authors":"D. Mendoza","doi":"10.2139/ssrn.3639452","DOIUrl":"https://doi.org/10.2139/ssrn.3639452","url":null,"abstract":"The main objective of the research is to analyze the cognitive attributes offered by Information and Communication Technologies to promote mathematical software as a model of teaching and learning. In the study, the software was used as a motivating didactic resource for the construction of meaningful learning. One hundred students of the first semester of Universidad Iberoamericana of Ecuador participated in this research. For the selection of the sample it was applied a non-probabilistic participatory type technique. The study was developed according to the approach of mixed methods of sequential explanatory design. The researcher organized the article in two phases: the first phase was quantitative. Quantitative results were obtained by applying a questionnaire to the students. The data demonstrated the need for change in university mathematics education. For students in the first semester, it was implemented the Wiris and Geogebra operational program during the qualitative phase. Moreover, the observation guide made it possible to collect qualitative information. The results of both phases were joined through the triangulation method. In conclusion, it is proposed the use of software as a model of teaching-learning process. It is highlighted the importance of active group knowledge sharing.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"294 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124223210","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: 22
The Azzalini Skew-t Information Matrix Evaluation and Use for Standard Error Calculations Azzalini歪斜信息矩阵的评估及其在标准误差计算中的应用
Mathematics eJournal Pub Date : 2018-09-30 DOI: 10.2139/ssrn.3258025
Chindhanai Uthaisaad, Doug Martin
{"title":"The Azzalini Skew-t Information Matrix Evaluation and Use for Standard Error Calculations","authors":"Chindhanai Uthaisaad, Doug Martin","doi":"10.2139/ssrn.3258025","DOIUrl":"https://doi.org/10.2139/ssrn.3258025","url":null,"abstract":"The Azzalini skew-t distributions are popular because of their theoretical foundation and the availability of computational methods in the R package sn. One difficulty with this skew-t family is that the elements of the expected information matrix do not have closed form analytic formulas. Thus, we developed a numerical integration method of computing the expected information matrix in the R package skewtInfo. The accuracy of our expected information matrix calculation method was confirmed by comparing the result with that obtained using an observed information matrix for a very large sample size. A Monte Carlo study to evaluate the accuracy of the finite-sample standard errors obtained with our expected information matrix calculation method, for the case of three realistic skew-t parameter vectors, indicates that use of the expected information matrix results in standard errors as accurate as, and sometimes a little more accurate than, use of an observed information matrix.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131711168","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
Gram Charlier and Edgeworth Expansion for Sample Variance 样本方差的Gram Charlier和Edgeworth展开式
Mathematics eJournal Pub Date : 2018-09-18 DOI: 10.2139/ssrn.3251324
E. Benhamou
{"title":"Gram Charlier and Edgeworth Expansion for Sample Variance","authors":"E. Benhamou","doi":"10.2139/ssrn.3251324","DOIUrl":"https://doi.org/10.2139/ssrn.3251324","url":null,"abstract":"In this paper, we derive a valid Edgeworth expansions for the Bessel corrected empirical variance when data are generated by a strongly mixing process whose distribution can be arbitrarily. The constraint of strongly mixing process makes the problem not easy. Indeed, even for a strongly mixing normal process, the distribution is unknown. Here, we do not assume any other assumption than a sufficiently fast decrease of the underlying distribution to make the Edgeworth expansion convergent. This results can obviously apply to strongly mixing normal process and provide an alternative to the work of Moschopoulos (1985) and Mathai (1982).","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120945731","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: 2
Selfsimilarity in Long Horizon Asset Returns 长期资产回报的自相似性
Mathematics eJournal Pub Date : 2018-08-08 DOI: 10.2139/ssrn.3102406
D. Madan, W. Schoutens
{"title":"Selfsimilarity in Long Horizon Asset Returns","authors":"D. Madan, W. Schoutens","doi":"10.2139/ssrn.3102406","DOIUrl":"https://doi.org/10.2139/ssrn.3102406","url":null,"abstract":"Daily return distributions are modeled by pure jump limit laws that are selfdecomposable laws. The returns may be seen as composed of a sum of independent and identically distributed increments or as a selfsimilar law scaling the sum of exponentially weighted past shocks or a combination thereof. To the extent the selfsimilar component is present and the scaling coefficient is above a half it is shown that long horizon returns may not converge to a normal distribution. Estimations conducted on 214 equity underliers over the period January 2007 to February 2017 support this lack of convergence to normality at very long horizons. An analysis of distributions embedded in option data shows that the convergence to normality is also halted risk neutrally. Selfsimilar components are estimated to have a physical half life between one or two days and a risk neutral half life around a year. In the long run markets are in an equilibrium state of motion engineered to avoid the evolution of good deals. The associated equilibrium solutions are illustrated. The implications of a selfsimilar scaling component for the equity bias, volatility and desirability of returns across horizons, horizon effects on expected returns, and Sharpe ratios are developed. Additionally long horizon return modeling is employed to construct alternative long horizon risk free rates using volatility targets.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"110 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114903427","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: 9
Bounds for the Diameter of the Weight Polytope 权重多面体直径的边界
Mathematics eJournal Pub Date : 2018-08-08 DOI: 10.2139/ssrn.3228524
Sascha Kurz
{"title":"Bounds for the Diameter of the Weight Polytope","authors":"Sascha Kurz","doi":"10.2139/ssrn.3228524","DOIUrl":"https://doi.org/10.2139/ssrn.3228524","url":null,"abstract":"A weighted game or a threshold function in general admits different weighted representations even if the sum of non-negative weights is fixed to one. Here we study bounds for the diameter of the corresponding weight polytope. It turns out that the diameter can be upper bounded in terms of the maximum weight and the quota or threshold. We apply those results to approximation results between power distributions, given by power indices, and weights.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"292 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134216706","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: 3
The IFRS17 Guide for the Perplexed Actuary IFRS17《困惑的精算师指南》
Mathematics eJournal Pub Date : 2018-07-29 DOI: 10.2139/ssrn.3222293
Anselm Fleischmann, Jonas Hirz
{"title":"The IFRS17 Guide for the Perplexed Actuary","authors":"Anselm Fleischmann, Jonas Hirz","doi":"10.2139/ssrn.3222293","DOIUrl":"https://doi.org/10.2139/ssrn.3222293","url":null,"abstract":"This paper provides a rigorous mathematical formulation of the main components within the building block approach (BBA) and the variable fee approach (VFA) in the IFRS17 standard as released in May 2017. The given actuarial model provides formulas for a precise depiction of the contractual service margin (CSM). A straightforward derivation of the insurance result is given. Quantitative aspects for the applicability of the VFA are introduced. Provided model extensions include the derivation of insurance revenue. Demystifying the complex standard, the paper illuminates critical passages, gives rise to potential actuarial approximations tackling undue efforts and provides a basis for implementation.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115664442","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
Conditional Expectiles, Time Consistency and Mixture Convexity Properties 条件质点，时间一致性和混合凸性
Mathematics eJournal Pub Date : 2018-07-11 DOI: 10.2139/ssrn.3009354
Fabio Bellini, V. Bignozzi, Giovanni Puccetti
{"title":"Conditional Expectiles, Time Consistency and Mixture Convexity Properties","authors":"Fabio Bellini, V. Bignozzi, Giovanni Puccetti","doi":"10.2139/ssrn.3009354","DOIUrl":"https://doi.org/10.2139/ssrn.3009354","url":null,"abstract":"We study conditional expectiles, defined as a natural generalisation of conditional expectations by means of the minimisation of an asymmetric quadratic loss function. We show that conditional expectiles can be equivalently characterised by a conditional first order condition and we derive their main properties. For possible applications as dynamic risk measures, we discuss their time consistency properties.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"185 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116519705","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: 16
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