Mathematics eJournal最新文献

{"title":"Hedge or Rebalance: Optimal Risk Management with Transaction Costs","authors":"Florent Gallien, S. Kassibrakis, S. Malamud","doi":"10.2139/ssrn.3230622","DOIUrl":"https://doi.org/10.2139/ssrn.3230622","url":null,"abstract":"We solve the problem of optimal risk management for an investor holding an illiquid, alpha-generating fund and hedging his/her position with a liquid futures contract. When the investor is subject to a lower bound on net return, he/she is forced to reduce the total risk of his/her portfolio after a loss. In this case, he/she faces a tradeoff of either paying the transaction costs and deleveraging or keeping his/her current position in the illiquid instrument and hedging away some of the risk while keeping the residual, unhedgeable risk on his/her balance sheet. We explicitly characterize this tradeoff and study its dependence on asset characteristics. In particular, we show that higher alpha and lower beta typically widen the no-trading zone, while the impact of volatility is ambiguous.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"56 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114859425","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}

{"title":"Dynamics of a Three Species Predator-Prey Delay Differential Model with Allee Effect and Holling Type-II Functional Response","authors":"H. Alsakaji, Fathalla A. Rihan, R. Chinnathambi","doi":"10.2139/ssrn.3273687","DOIUrl":"https://doi.org/10.2139/ssrn.3273687","url":null,"abstract":"In recent years, predator-prey models appearing in various fields of mathematical biology have been proposed and studied extensively. In this paper, we propose a delay differential model for predator-prey systems of one predator and two preys with cooperation/competition among the preys. The growth of both prey populations is subjected to the Allee effect in the logistic terms (the growth rate increases with the population density while it decreases at larger densities), with Holling type I and II functional responses with the predators. Discrete time delays are incorporated into the model to justify time required by predator to interact with the preys. We study the existence of positive equilibrium points and their asymptotic stabilities. Hopfbifurcations are obtained in terms of critical values of time delays. The system may have a stable periodic orbit, depending on parameter values. The presence of Allee terms and time delays in the model improves the stability of the solutions and enriches the dynamics of the model. Some numerical examples and simulations are provided to validate the derived theoretical results.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125320026","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}

{"title":"Fractional-Order Diffusion Model for Social Networks","authors":"Piotr Sakrajda, Michał Sławomir Wiraszka","doi":"10.2139/ssrn.3271330","DOIUrl":"https://doi.org/10.2139/ssrn.3271330","url":null,"abstract":"One of the most common areas of real world fractional-order model applications are diffusion processes. In the paper the attempt to use fractional-order diffusion equation to model information diffusion in a social network is made. The example dataset consist of citations for over 34000 arXiv papers. Basic diffusive fractional-order model is compared with Monte Carlo simulation of the flow of information from a particular node (paper) within the network. Experiments shown that the model of diffusion within network can be accurately fitted to the results obtained with the numerical method. Order of the obtained model (from 0.05 to 0.4 depending on the source node of diffusion) indicates, that the investigated citation network is a highly superdiffusive system. The results can be significant for the future works, including fractional-order generalization of epidemic models or diffusion in variable order networks.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"74 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129746127","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}

{"title":"On the Regional Controllability for Hadamard-Caputo Fractional Ultra-Slow Diffusion Processes","authors":"Ruiyang Cai, Fudong Ge, Y. Chen, C. Kou","doi":"10.2139/ssrn.3282725","DOIUrl":"https://doi.org/10.2139/ssrn.3282725","url":null,"abstract":"In this article, we address the regional controllability problem for ultra-slow diffusion processes governed by Hadamard-Caputo time fractional diffusion systems. Some necessary and sufficient conditions on both regional exact controllability and regional approximate controllability of the considered systems are first obtained. Secondly, we provide a necessary and sufficient condition on the minimum number of the actuators to achieve the regional approximate controllability. Moreover, by applying the Hilbert Uniqueness Method (HUM), the optimal actuators with minimum energy can be chosen among the whole admissible ones. Finally, an example is given to illustrate our results.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127882102","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}

{"title":"Disproving Market Demand and Market Supply","authors":"Hak Choi","doi":"10.2139/SSRN.3203158","DOIUrl":"https://doi.org/10.2139/SSRN.3203158","url":null,"abstract":"This paper disproves the concepts of market demand and market supply. It discovers two suspicions that such concepts may be wrong: they deliver uncertain equilibrium or infinite price, and their elasticity preservation creates an identity crisis. In contrast, this paper works out how incessant arbitrage by laissez faire people generates market price, to render market demand or market supply unnecessary. Market demand or supply, if any, represents autocracy, suppresses individuality, and hence should not belong to Economics.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"65 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121026680","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}

{"title":"Minorization-Maximization (MM) Algorithm for Semiparametric Logit Models: Bottlenecks, Extensions, and Comparisons","authors":"P. Bansal, Ricardo A. Daziano, E. Guerra","doi":"10.2139/ssrn.3156835","DOIUrl":"https://doi.org/10.2139/ssrn.3156835","url":null,"abstract":"Motivated by the promising performance of alternative estimation methods for mixed logit models, in this paper we derive, implement, and test expectation-maximization (EM) and minorization-maximization (MM) algorithms to estimate the semiparametric logit mixed logit (LML) and mixture-of-normals multinomial logit (MON-MNL) models. In particular, we show that the reported computational efficiency of the MM algorithm is actually lost for large choice sets. Because the logit link that represents the parameter space in LML is intrinsically treated as a large choice set, the MM algorithm for LML actually becomes unfeasible to use in practice. We thus propose a faster MM algorithm that revisits a simple step-size correction. In a Monte Carlo study, we compare the maximum simulated likelihood estimator (MSLE) with the algorithms that we derive to estimate LML and MON-MNL models. Whereas in LML estimation alternative algorithms are computationally uncompetitive with MSLE, the faster-MM algorithm appears emulous in MON-MNL estimation. Both algorithms – faster-MM and MSLE – could recover parameters as well as standard errors at a similar precision in both models. We further show that parallel computation could reduce estimation time of faster-MM by 45% to 80%. Even though faster-MM could not surpass MSLE with analytical gradient (because MSLE also leveraged similar computational gains), parallel faster-MM is a competitive replacement to MSLE for MON-MNL that obviates computation of complex analytical gradients, which is a very attractive feature to integrate it into a flexible estimation software. We also compare different algorithms in an empirical application to estimate consumer’s willingness to adopt electric motorcycles in Solo, Indonesia. The results of the empirical application are consistent with those of the Monte Carlo study.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125120182","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}

{"title":"Generalized Correlation Measures of Causality and Forecasts of the VIX Using Non-Linear Models","authors":"D. Allen, Vincent J. Hooper","doi":"10.2139/ssrn.3191737","DOIUrl":"https://doi.org/10.2139/ssrn.3191737","url":null,"abstract":"This paper features an analysis of causal relations between the daily VIX, S&P500 and the daily realised volatility (RV) of the S&P500 sampled at 5 min intervals, plus the application of an Artificial Neural Network (ANN) model to forecast the future daily value of the VIX. Causal relations are analysed using the recently developed concept of general correlation Zheng et al. and Vinod. The neural network analysis is performed using the Group Method of Data Handling (GMDH) approach. The results suggest that causality runs from lagged daily RV and lagged continuously compounded daily return on the S&P500 index to the VIX. Sample tests suggest that an ANN model can successfully predict the daily VIX using lagged daily RV and lagged daily S&P500 Index continuously compounded returns as inputs.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115385249","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}

{"title":"Problem Solving with and without Mathematics: An Idiot’s Guide to the Idiots Inside All of Us, For Business and Everything Else (Presentation Slides)","authors":"R. Kashyap","doi":"10.2139/SSRN.3190792","DOIUrl":"https://doi.org/10.2139/SSRN.3190792","url":null,"abstract":"We consider the essential elements of problem solving that will be useful from a business perspective in addition to being applicable to other areas of life. The discussion revolves around certain well-known problems from real life scenarios and a demonstration of how trial and error techniques have been used to solve these problems. We then pick simple mathematical tools that be applied to solve these problems. The idea is to understand how the intuition that all of us possess can be developed and elegant solutions can be obtained by applying simple mathematical results. The goal is to introduce to everyone (and help them develop an appreciation of) some basic mathematical techniques that can be useful towards the solving of real life problems.<br><br>This course (set of discussions) is meant to be completely self-contained and all the required concepts will be introduced and developed in the sections below. There will be topics covered from many fields including: marketing, psychology, operations, management, finance, literature, artificial intelligence, economics, physics, biology, etc. The essential requirement for reading this course is to have curiosity and a willingness to participate in the exercises with the objective of trying to find solutions independently. This course is open to people from all disciplines. The only mathematical skill required for this course is familiarity with addition.<br><br>At the end of this course, students (almost everyone in society if we define students as someone that wants to continue learning) will: Understand the importance of trial and error in solving problems. Develop an appreciation of simple mathematical tools that can complement the intuition behind solving business problems. Develop the ability to approach new problems and come up new tools that might be necessary, on their own. Comprehend how new problems keep arising in real life situations as old problems are solved and the importance of human behavior in the creation and solution of many problems. (An unintended consequence might be starting to believe that mathematics can become simple with minimal effort to understand the steps and the notation). Develop the skills to apply these techniques to business situations. <br>","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121396849","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}

{"title":"On the Formulation of the Problem of Optimal Control of Production Parameters Using a Two-Level Model of the Production Process","authors":"O. Pihnastyi, Oksana Parachnevych","doi":"10.2139/ssrn.3242406","DOIUrl":"https://doi.org/10.2139/ssrn.3242406","url":null,"abstract":"Using a statistical approach, widespread in natural sciences, a two-level model to control the parameters of the flow line production system has been built. The state of the system is given by the amounts of sets of the objects of labour. The state of the subject of labour is given by a point in the phase space. The function of the distribution of objects of labour by the state is introduced and the kinetic equation for the distribution function is written. Now we have closed system of dynamical equations for parameters of flow production line. The null and the first moments of the distribution function of labour objects in terms of the state characterize the magnitude of inter-operational stocks and the rate of processing of labour objects from operations of the technological route and are the main parameters of the management of the production line. The limiting transition from the kinetic description of the state of objects of labour to the stream description of the processing of objects of labour is accomplished. Integration of the kinetic equation by the states of the objects of labour made it possible to construct a closed system of balance equations for the parameters of the production line. The task of optimal control of the flow parameters of the production line has been set. The balance equations for the moments of the distribution function of objects of labour by states determine the constraint equations in the control problem","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130215193","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}

{"title":"Computing the Cornish Fisher Expansion Moments Using Hermite Polynomials: A Note","authors":"Didier Maillard","doi":"10.2139/ssrn.3187286","DOIUrl":"https://doi.org/10.2139/ssrn.3187286","url":null,"abstract":"The computation of the moments of the Cornish Fisher expansion, which is an important prerequisite for a proper use, is a rather cumbersome and tedious task. This short paper explores if a detour through the Hermite polynomials is helpful for that computation. The answer is a qualified yes.","PeriodicalId":260073,"journal":{"name":"Mathematics eJournal","volume":"113 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124267436","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}