{"title":"Optimal inventory policy with fixed and proportional transaction costs under a risk constraint","authors":"S.Y. Wang , K.F.C. Yiu , K.L. Mak","doi":"10.1016/j.mcm.2012.03.009","DOIUrl":"10.1016/j.mcm.2012.03.009","url":null,"abstract":"<div><p>The traditional inventory models focus on characterizing replenishment policies in order to maximize the total expected profit or to minimize the expected total cost over a planned horizon. However, for many companies, total inventory costs could be accounting for a fairly large amount of invested capital. In particular, raw material inventories should be viewed as a type of invested asset for a manufacturer with suitable risk control. This paper is intended to provide this perspective on inventory management that treats inventory problems within a wider context of financial risk management. In view of this, the optimal inventory problem under a VaR constraint is studied. The financial portfolio theory has been used to model the dynamics of inventories. A diverse portfolio consists of raw material inventories, which involve market risk because of price fluctuations as well as a risk-free bank account. The value-at-risk measure is applied thereto to control the inventory portfolio’s risk. The objective function is to maximize the utility of total portfolio value. In this model, the ordering cost is assumed to be fixed and the selling cost is proportional to the value. The inventory control problem is thus formulated as a continuous stochastic optimal control problem with fixed and proportional transaction costs under a continuous value-at-risk (VaR) constraint. The optimal inventory policies are derived by using stochastic optimal control theory and the optimal inventory level is reviewed and adjusted continuously. A numerical algorithm is proposed and the results illustrate how the raw material price, inventory level and VaR constraint are interrelated.</p></div>","PeriodicalId":49872,"journal":{"name":"Mathematical and Computer Modelling","volume":"58 9","pages":"Pages 1595-1614"},"PeriodicalIF":0.0,"publicationDate":"2013-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.mcm.2012.03.009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80925658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Herick Fernando Moralles , Daisy Aparecida do Nascimento Rebelatto , Alexandre Sartoris
{"title":"Parametric VaR with goodness-of-fit tests based on EDF statistics for extreme returns","authors":"Herick Fernando Moralles , Daisy Aparecida do Nascimento Rebelatto , Alexandre Sartoris","doi":"10.1016/j.mcm.2013.07.002","DOIUrl":"10.1016/j.mcm.2013.07.002","url":null,"abstract":"<div><p>Parametric VaR (Value-at-Risk) is widely used due to its simplicity and easy calculation. However, the normality assumption, often used in the estimation of the parametric VaR, does not provide satisfactory estimates for risk exposure. Therefore, this study suggests a method for computing the parametric VaR based on goodness-of-fit tests using the empirical distribution function (EDF) for extreme returns, and compares the feasibility of this method for the banking sector in an emerging market and in a developed one. The paper also discusses possible theoretical contributions in related fields like enterprise risk management (ERM).</p></div>","PeriodicalId":49872,"journal":{"name":"Mathematical and Computer Modelling","volume":"58 9","pages":"Pages 1648-1658"},"PeriodicalIF":0.0,"publicationDate":"2013-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.mcm.2013.07.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77235719","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Optimal investment with a corporate bond","authors":"Shibo Bian , Hailong Liu","doi":"10.1016/j.mcm.2012.05.001","DOIUrl":"10.1016/j.mcm.2012.05.001","url":null,"abstract":"<div><p>The present paper analyzes the optimal investment strategy in a corporate (defaultable) bond, a stock and a bank account in a continuous time model. We model the corporate bond price through a reduced-form approach and solve the dynamics of its price. The optimal investment process will be worked out first with a general risk-averse utility function, and then an optimal strategy with CARA utility will be presented using martingale methods. The optimal investment strategy is analyzed numerically for the CARA utility.</p></div>","PeriodicalId":49872,"journal":{"name":"Mathematical and Computer Modelling","volume":"58 9","pages":"Pages 1615-1624"},"PeriodicalIF":0.0,"publicationDate":"2013-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.mcm.2012.05.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75576443","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Measuring the capital charge for operational risk of a bank with the large deviation approach","authors":"Zhaoyang Lu","doi":"10.1016/j.mcm.2013.07.001","DOIUrl":"10.1016/j.mcm.2013.07.001","url":null,"abstract":"<div><p>In this paper, the large deviation approach for computing the capital charge for operational risk of a bank is explored. Firstly, the negatively-associated structure is utilized to measure the dependence between distinct operational loss cells. Secondly, the lower and upper bounds of the tail distribution function of total aggregated loss processes are determined. In addition, first order approximations using a value-at-risk measure are derived. Finally, an important example calculating the capital charge for operational risk under the class of a heavy-tailed distribution is provided.</p></div>","PeriodicalId":49872,"journal":{"name":"Mathematical and Computer Modelling","volume":"58 9","pages":"Pages 1634-1647"},"PeriodicalIF":0.0,"publicationDate":"2013-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.mcm.2013.07.001","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78282884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Simultaneous quantitative determination of Amlodipine and Atorvastatin in tablets using artificial neural networks","authors":"Mahmoud Reza Sohrabi , Parviz Abdolmaleki , Maryam Dehroudi","doi":"10.1016/j.mcm.2011.11.034","DOIUrl":"10.1016/j.mcm.2011.11.034","url":null,"abstract":"<div><p>Simultaneous spectrophotometric estimation of Atorvastatin Calcium and Amlodipine Besylate in Amostatine<sup>®</sup> tablets were performed using UV–Vis spectroscopic and Artificial Neural Networks (ANN). Absorption spectra of two components were recorded in 200–350 (nm) wavelengths region with an interval of 4 nm. The calibration models were thoroughly evaluated at several concentration levels using the spectra of synthetic binary mixture (prepared using orthogonal design). Three layers feed-forward neural networks using the back-propagation algorithm (B.P) has been employed for building and testing models. Several parameters such as the number of neurons in the hidden layer, learning rate and the number of epochs were optimized. A general statistic function, Sum Square Error (SSE), was selected to evaluate the training process of ANN. The single Relative Standard Error (RSE) (%) of prediction for each component in real sample was calculated as 0.62 and 2.00 for Atorvastatin and Amlodipine, respectively. The results showed a very good agreement between true values and predicted concentration values. The proposed procedure is a simple, precise and convenient method for the determination of Atorvastatin and Amlodipine in commercial tablets.</p></div>","PeriodicalId":49872,"journal":{"name":"Mathematical and Computer Modelling","volume":"58 9","pages":"Pages 1588-1594"},"PeriodicalIF":0.0,"publicationDate":"2013-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.mcm.2011.11.034","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87732438","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Bargaining in supply chain with price and promotional effort dependent demand","authors":"Desheng Dash Wu","doi":"10.1016/j.mcm.2010.12.035","DOIUrl":"10.1016/j.mcm.2010.12.035","url":null,"abstract":"<div><p>This paper investigates the bargaining equilibrium behavior of an industry with two competing supply chains. The demand in each supply chain is modeled using the downward-sloping linear function with respect to both price and promotional effort. The optimality is established through Nash bargaining when the two competing manufacturers distribute through two independent competing retailers. We show, when both price and promotional effort dependent demand is present, that both the traditional Manufacturer Stackelberg (MS) and the Vertical Integration (VI) are special cases of our Nash bargaining game. We conclude that both sales promotional service and price dominates bargaining on only one factor. We yield several conclusions about the provision of promotional service level by each supply chain to coordinate the channel.</p></div>","PeriodicalId":49872,"journal":{"name":"Mathematical and Computer Modelling","volume":"58 9","pages":"Pages 1659-1669"},"PeriodicalIF":0.0,"publicationDate":"2013-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.mcm.2010.12.035","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85813807","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Several consensus protocols with memory of multi-agent systems","authors":"Xin-Lei Feng , Ting-Zhu Huang , Jin-Liang Shao","doi":"10.1016/j.mcm.2012.09.009","DOIUrl":"10.1016/j.mcm.2012.09.009","url":null,"abstract":"<div><p>Financial risk management has focused on banking, accounting, and finance, and applied all kinds types of models to avoid those specific forms of risk. Risk management may be dealt with using the model of multi-agent systems. In this paper, we consider single-integrator kinematics and double-order-integrator dynamics consensus protocols. These consensus protocols with memory are presented by introducing the last state information (such as position, velocity) of the multi-agent. The numerical results show that these protocols have higher convergence speed.</p></div>","PeriodicalId":49872,"journal":{"name":"Mathematical and Computer Modelling","volume":"58 9","pages":"Pages 1625-1633"},"PeriodicalIF":0.0,"publicationDate":"2013-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.mcm.2012.09.009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90373169","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"The impact of distribution on value-at-risk measures","authors":"David L. Olson , Desheng Wu","doi":"10.1016/j.mcm.2011.06.053","DOIUrl":"10.1016/j.mcm.2011.06.053","url":null,"abstract":"<div><p>Value at risk is a popular approach to aid financial risk management. Questions about the appropriateness of the measure have arisen since the related 2008 bubble collapses in some US housing markets and the global financial market. These questions include the presence of fat tails and their impact. This paper compares results based upon assumptions of normality and logistic distributions, comparing portfolios generated with various probabilistic models. Computations are applied to real stock data. Optimization models are described, with simulation models evaluating comparative model performance. Chi-square tests indicated that logistic distribution better fit the data than the normal distribution. The error implied by value-at-risk assumptions is demonstrated through Monte Carlo simulation.</p></div>","PeriodicalId":49872,"journal":{"name":"Mathematical and Computer Modelling","volume":"58 9","pages":"Pages 1670-1676"},"PeriodicalIF":0.0,"publicationDate":"2013-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.mcm.2011.06.053","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84044887","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A new multi-symplectic Euler box scheme for the BBM equation","authors":"Haochen Li , Jianqiang Sun","doi":"10.1016/j.mcm.2013.06.012","DOIUrl":"10.1016/j.mcm.2013.06.012","url":null,"abstract":"<div><p>A new scheme for the BBM equation with the accuracy order of <span><math><mi>O</mi><mrow><mo>(</mo><mo>△</mo><msup><mrow><mi>t</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><mo>△</mo><msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></mrow></math></span> is proposed. The multi-symplectic conservation property of the new scheme is proved. The backward error analysis of the new scheme is implemented. The solitary wave evolution behaviors are simulated by the new scheme. The new multi-symplectic Euler box scheme is compared with the classical Euler box scheme and the Preissman box scheme in preserving the conservation properties of the BBM equation and the computation cost.</p></div>","PeriodicalId":49872,"journal":{"name":"Mathematical and Computer Modelling","volume":"58 7","pages":"Pages 1489-1501"},"PeriodicalIF":0.0,"publicationDate":"2013-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.mcm.2013.06.012","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91400652","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Spreading speeds and travelling waves for non-monotone time-delayed 2D lattice systems","authors":"Zhi-Xian Yu , Weiguo Zhang , Xiaoming Wang","doi":"10.1016/j.mcm.2013.06.009","DOIUrl":"10.1016/j.mcm.2013.06.009","url":null,"abstract":"<div><p>In this paper, a non-monotone time delayed 2D lattice system with global interaction is studied. The important feature of the model is the reflection of the joint effect of the diffusion dynamics, the nonlocal delayed effect and the direction of propagation. The existence of travelling waves for the wave speed <span><math><mi>c</mi><mo>≥</mo><msub><mrow><mi>c</mi></mrow><mrow><mo>∗</mo></mrow></msub><mrow><mo>(</mo><mi>θ</mi><mo>)</mo></mrow></math></span> is established by Schauder’s fixed point theorem and a limiting argument, where <span><math><mi>θ</mi></math></span> is any fixed direction of propagation. The spreading speed is investigated by comparison arguments and a fluctuation method. It is also shown that the spreading speed coincides with the minimal wave speed along every direction. Particularly, letting the direction of propagation <span><math><mi>θ</mi><mo>=</mo><mn>0</mn></math></span> or <span><math><mfrac><mrow><mi>π</mi></mrow><mrow><mn>2</mn></mrow></mfrac></math></span>, the wave profile equation of the 2D lattice system can reduce to the wave profile equation of 1D lattice system and therefore, our results can cover the previous works.</p></div>","PeriodicalId":49872,"journal":{"name":"Mathematical and Computer Modelling","volume":"58 7","pages":"Pages 1510-1521"},"PeriodicalIF":0.0,"publicationDate":"2013-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.mcm.2013.06.009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74377881","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}