The presented study elaborates a multi-server priority queueing model considering the preemptive repeat policy and phase-type distribution (begin{document}$ P!H $end{document}) for retrial process. The incoming heterogeneous calls are categorized as handoff calls and new calls. The arrival and service processes of both types of calls follow marked Markovian arrival process (begin{document}$ M!M!A!P $end{document}) and begin{document}$ P!H $end{document} distribution with distinct parameters, respectively. An arriving new call will be blocked when all the channels are occupied, and consequently will join the orbit (virtual space) to retry following begin{document}$ P!H $end{document} distribution. When all the channels are occupied and a handoff call arrives at the system, out of the following two scenarios, one might take place. In the first scenario, if all the channels are occupied with handoff calls, the arriving handoff call will be lost from the system. While in the second one, if all the channels are occupied and at least one of them is serving a new call, the arriving handoff call will be provided service by using preemptive priority over that new call and the preempted new call will join the orbit. Behaviour of the proposed system is modelled by the level dependent quasi-birth-death begin{document}$ (L!D!Q!B!D) $end{document} process. The expressions of various performance measures have been derived for the numerical illustration. An optimization problem for optimal channel allocation and traffic control has been formulated and dealt by employing appropriate heuristic approaches.
The presented study elaborates a multi-server priority queueing model considering the preemptive repeat policy and phase-type distribution (begin{document}$ P!H $end{document}) for retrial process. The incoming heterogeneous calls are categorized as handoff calls and new calls. The arrival and service processes of both types of calls follow marked Markovian arrival process (begin{document}$ M!M!A!P $end{document}) and begin{document}$ P!H $end{document} distribution with distinct parameters, respectively. An arriving new call will be blocked when all the channels are occupied, and consequently will join the orbit (virtual space) to retry following begin{document}$ P!H $end{document} distribution. When all the channels are occupied and a handoff call arrives at the system, out of the following two scenarios, one might take place. In the first scenario, if all the channels are occupied with handoff calls, the arriving handoff call will be lost from the system. While in the second one, if all the channels are occupied and at least one of them is serving a new call, the arriving handoff call will be provided service by using preemptive priority over that new call and the preempted new call will join the orbit. Behaviour of the proposed system is modelled by the level dependent quasi-birth-death begin{document}$ (L!D!Q!B!D) $end{document} process. The expressions of various performance measures have been derived for the numerical illustration. An optimization problem for optimal channel allocation and traffic control has been formulated and dealt by employing appropriate heuristic approaches.
{"title":"Optimization of traffic control in $ MMAPmathit{[2]}/PHmathit{[2]}/S$ priority queueing model with $ PH $ retrial times and the preemptive repeat policy","authors":"R. Raj, Vidyottama Jain","doi":"10.3934/jimo.2022044","DOIUrl":"https://doi.org/10.3934/jimo.2022044","url":null,"abstract":"<p style='text-indent:20px;'>The presented study elaborates a multi-server priority queueing model considering the preemptive repeat policy and phase-type distribution (<inline-formula><tex-math id=\"M3\">begin{document}$ P!H $end{document}</tex-math></inline-formula>) for retrial process. The incoming heterogeneous calls are categorized as handoff calls and new calls. The arrival and service processes of both types of calls follow marked Markovian arrival process (<inline-formula><tex-math id=\"M4\">begin{document}$ M!M!A!P $end{document}</tex-math></inline-formula>) and <inline-formula><tex-math id=\"M5\">begin{document}$ P!H $end{document}</tex-math></inline-formula> distribution with distinct parameters, respectively. An arriving new call will be blocked when all the channels are occupied, and consequently will join the orbit (virtual space) to retry following <inline-formula><tex-math id=\"M6\">begin{document}$ P!H $end{document}</tex-math></inline-formula> distribution. When all the channels are occupied and a handoff call arrives at the system, out of the following two scenarios, one might take place. In the first scenario, if all the channels are occupied with handoff calls, the arriving handoff call will be lost from the system. While in the second one, if all the channels are occupied and at least one of them is serving a new call, the arriving handoff call will be provided service by using preemptive priority over that new call and the preempted new call will join the orbit. Behaviour of the proposed system is modelled by the level dependent quasi-birth-death <inline-formula><tex-math id=\"M7\">begin{document}$ (L!D!Q!B!D) $end{document}</tex-math></inline-formula> process. The expressions of various performance measures have been derived for the numerical illustration. An optimization problem for optimal channel allocation and traffic control has been formulated and dealt by employing appropriate heuristic approaches.</p>","PeriodicalId":347719,"journal":{"name":"Journal of Industrial & Management Optimization","volume":"213 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129435582","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A Pareto eigenvalue of a tensor begin{document}$ {mathcal A} $end{document} of order begin{document}$ m $end{document} and dimension begin{document}$ n $end{document} is a real number begin{document}$ lambda $end{document} for which the complementarity problem
admits a nonzero solution begin{document}$ {mathbf x}in mathbb{R}^n $end{document}, where begin{document}$ {mathcal E} $end{document} is an identity tensor. In this paper, we investigate some basic properties of Pareto eigenvalues, including an equivalent condition for the existence of strict Pareto eigenvalues and the nonnegative conditions of Pareto eigenvalues. Then we focus on the estimation of the bounds of Pareto eigenvalues. Specifically, we propose several Pareto eigenvalue inclusion intervals, and discuss the relationships among them and the known result, which demonstrate that the inclusion intervals obtained are tighter than the known one. Finally, as an application of an achieved inclusion intervals, we propose a sufficient condition for judging that a tensor is strictly copositive.
A Pareto eigenvalue of a tensor begin{document}$ {mathcal A} $end{document} of order begin{document}$ m $end{document} and dimension begin{document}$ n $end{document} is a real number begin{document}$ lambda $end{document} for which the complementarity problem begin{document}$ mathbf{0}leq {mathbf x} bot (lambda{mathcal E}{mathbf x}^{m-1}- {mathcal A}{mathbf x}^{m-1}) geq mathbf{0} $end{document} admits a nonzero solution begin{document}$ {mathbf x}in mathbb{R}^n $end{document}, where begin{document}$ {mathcal E} $end{document} is an identity tensor. In this paper, we investigate some basic properties of Pareto eigenvalues, including an equivalent condition for the existence of strict Pareto eigenvalues and the nonnegative conditions of Pareto eigenvalues. Then we focus on the estimation of the bounds of Pareto eigenvalues. Specifically, we propose several Pareto eigenvalue inclusion intervals, and discuss the relationships among them and the known result, which demonstrate that the inclusion intervals obtained are tighter than the known one. Finally, as an application of an achieved inclusion intervals, we propose a sufficient condition for judging that a tensor is strictly copositive.
{"title":"Pareto eigenvalue inclusion intervals for tensors","authors":"Yang Xu, Zhenghai Huang","doi":"10.3934/jimo.2022035","DOIUrl":"https://doi.org/10.3934/jimo.2022035","url":null,"abstract":"<p style='text-indent:20px;'>A Pareto eigenvalue of a tensor <inline-formula><tex-math id=\"M1\">begin{document}$ {mathcal A} $end{document}</tex-math></inline-formula> of order <inline-formula><tex-math id=\"M2\">begin{document}$ m $end{document}</tex-math></inline-formula> and dimension <inline-formula><tex-math id=\"M3\">begin{document}$ n $end{document}</tex-math></inline-formula> is a real number <inline-formula><tex-math id=\"M4\">begin{document}$ lambda $end{document}</tex-math></inline-formula> for which the complementarity problem</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id=\"FE1\"> begin{document}$ mathbf{0}leq {mathbf x} bot (lambda{mathcal E}{mathbf x}^{m-1}- {mathcal A}{mathbf x}^{m-1}) geq mathbf{0} $end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>admits a nonzero solution <inline-formula><tex-math id=\"M5\">begin{document}$ {mathbf x}in mathbb{R}^n $end{document}</tex-math></inline-formula>, where <inline-formula><tex-math id=\"M6\">begin{document}$ {mathcal E} $end{document}</tex-math></inline-formula> is an identity tensor. In this paper, we investigate some basic properties of Pareto eigenvalues, including an equivalent condition for the existence of strict Pareto eigenvalues and the nonnegative conditions of Pareto eigenvalues. Then we focus on the estimation of the bounds of Pareto eigenvalues. Specifically, we propose several Pareto eigenvalue inclusion intervals, and discuss the relationships among them and the known result, which demonstrate that the inclusion intervals obtained are tighter than the known one. Finally, as an application of an achieved inclusion intervals, we propose a sufficient condition for judging that a tensor is strictly copositive.</p>","PeriodicalId":347719,"journal":{"name":"Journal of Industrial & Management Optimization","volume":"12 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127423082","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}
In order to achieve the goal of "carbon neutral" development, under the conditions of carbon quota trading policy, consumers' preference for fresh agricultural products and low-carbon preference, this paper discusses the equilibrium decision-making problem of a two-level fresh agricultural products supply chain. And the cost sharing contract and the two-part pricing contract are introduced to coordinate the supply chain. The results show that: the fresh-keeping and low-carbon efforts made by fresh produce suppliers are related to consumers' preferences, fresh-keeping costs, low-carbon costs, fresh-keeping carbon emission factors, and carbon reduction efficiency; under certain conditions, both the cost sharing contract and the two-part pricing contract can coordinate the supply chain of fresh agricultural products; given certain costs and carbon reduction efficiency, which contract retailers choose depends on consumers' consumption preferences and the size of the supplier's initial carbon emissions; when both contracts are valid, it is more advantageous for the retailer to choose two-part pricing contract; the higher the carbon trading price, the better the incentive effect on suppliers' fresh-keeping efforts and low-carbon efforts.
{"title":"Fresh agricultural products supply chain coordination considering consumers' dual preferences under carbon cap-and-trade mechanism","authors":"Yang Yang, G. Yao","doi":"10.3934/jimo.2022032","DOIUrl":"https://doi.org/10.3934/jimo.2022032","url":null,"abstract":"In order to achieve the goal of \"carbon neutral\" development, under the conditions of carbon quota trading policy, consumers' preference for fresh agricultural products and low-carbon preference, this paper discusses the equilibrium decision-making problem of a two-level fresh agricultural products supply chain. And the cost sharing contract and the two-part pricing contract are introduced to coordinate the supply chain. The results show that: the fresh-keeping and low-carbon efforts made by fresh produce suppliers are related to consumers' preferences, fresh-keeping costs, low-carbon costs, fresh-keeping carbon emission factors, and carbon reduction efficiency; under certain conditions, both the cost sharing contract and the two-part pricing contract can coordinate the supply chain of fresh agricultural products; given certain costs and carbon reduction efficiency, which contract retailers choose depends on consumers' consumption preferences and the size of the supplier's initial carbon emissions; when both contracts are valid, it is more advantageous for the retailer to choose two-part pricing contract; the higher the carbon trading price, the better the incentive effect on suppliers' fresh-keeping efforts and low-carbon efforts.","PeriodicalId":347719,"journal":{"name":"Journal of Industrial & Management Optimization","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125102624","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}
Qisuai Wang, Pei Li, Ting Lei, Xiaofeng Liu, G. Cai
The finite-horizon two-person zero-sum differential game is a significant technology to solve the finite-horizon spacecraft pursuit-evasion game (SPE game). Considering that the saddle point solution of the differential game usually results in solving a high-dimensional (24 dimensional in this paper) two-point boundary value problem (TPBVP) that is challengeable, a dimension-reduction method is proposed in this paper to simplify the solution of the 24-dimensional TPBVP related to the finite-horizon SPE game and to improve the efficiency of the saddle point solution. In this method, firstly, the 24-dimensional TPBVP can be simplified to a 12-dimensional TPBVP by using the linearization of the spacecraft dynamics; then the adjoint variables associated with the relative state variables between the pursuer and evader can be expressed in the form of state transition; after that, based on the necessary conditions for the saddle point solution and the adjoint variables in the form of state transition, the 12-dimensional TPBVP can be transformed into the solving of 6-dimensional nonlinear equations; finally, a hybrid numerical algorithm is developed to solve the nonlinear equations so as to obtain the saddle point solution. The simulation results show that the proposed method can effectively obtain the saddle point solution and is robust to the interception time, the orbital altitude and the initial relative states between the pursuer and evader.
{"title":"A Dimension-reduction method for the finite-horizon spacecraft pursuit-evasion game","authors":"Qisuai Wang, Pei Li, Ting Lei, Xiaofeng Liu, G. Cai","doi":"10.3934/jimo.2022028","DOIUrl":"https://doi.org/10.3934/jimo.2022028","url":null,"abstract":"The finite-horizon two-person zero-sum differential game is a significant technology to solve the finite-horizon spacecraft pursuit-evasion game (SPE game). Considering that the saddle point solution of the differential game usually results in solving a high-dimensional (24 dimensional in this paper) two-point boundary value problem (TPBVP) that is challengeable, a dimension-reduction method is proposed in this paper to simplify the solution of the 24-dimensional TPBVP related to the finite-horizon SPE game and to improve the efficiency of the saddle point solution. In this method, firstly, the 24-dimensional TPBVP can be simplified to a 12-dimensional TPBVP by using the linearization of the spacecraft dynamics; then the adjoint variables associated with the relative state variables between the pursuer and evader can be expressed in the form of state transition; after that, based on the necessary conditions for the saddle point solution and the adjoint variables in the form of state transition, the 12-dimensional TPBVP can be transformed into the solving of 6-dimensional nonlinear equations; finally, a hybrid numerical algorithm is developed to solve the nonlinear equations so as to obtain the saddle point solution. The simulation results show that the proposed method can effectively obtain the saddle point solution and is robust to the interception time, the orbital altitude and the initial relative states between the pursuer and evader.","PeriodicalId":347719,"journal":{"name":"Journal of Industrial & Management Optimization","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127983855","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}
Jingzhen Liu, S. Yan, Shan (Victor) Jiang, Jiaqin Wei
This paper studies the optimal investment, consumption and life insurance decisions of an agent under stochastic differential utility. The optimal choice is obtained through dynamic programming method. We state a verification theorem using the Hamilton-Jacobi-Bellman equation. For the special case of Epstein-Zin preferences, we derive the analytical solution to the problem. Moreover, we explore the effects of habit formation and of the elasticity of the utility function on the optimal decision through a numerical simulation based on Chinese mortality rates. We show that habit formation does not change the basic shape of the consumption and bequest curves. With habit formation, the optimal consumption curve moves up with lower initial consumption, while the bequest curve moves down. Increasing the value of initial habit formation slightly decreases both optimal consumption and bequests. The changes in the habit formation parameters have a greater impact on the curves than does a change in the initial habit formation.
{"title":"Optimal investment, consumption and life insurance strategies under stochastic differential utility with habit formation","authors":"Jingzhen Liu, S. Yan, Shan (Victor) Jiang, Jiaqin Wei","doi":"10.3934/jimo.2022040","DOIUrl":"https://doi.org/10.3934/jimo.2022040","url":null,"abstract":"This paper studies the optimal investment, consumption and life insurance decisions of an agent under stochastic differential utility. The optimal choice is obtained through dynamic programming method. We state a verification theorem using the Hamilton-Jacobi-Bellman equation. For the special case of Epstein-Zin preferences, we derive the analytical solution to the problem. Moreover, we explore the effects of habit formation and of the elasticity of the utility function on the optimal decision through a numerical simulation based on Chinese mortality rates. We show that habit formation does not change the basic shape of the consumption and bequest curves. With habit formation, the optimal consumption curve moves up with lower initial consumption, while the bequest curve moves down. Increasing the value of initial habit formation slightly decreases both optimal consumption and bequests. The changes in the habit formation parameters have a greater impact on the curves than does a change in the initial habit formation.","PeriodicalId":347719,"journal":{"name":"Journal of Industrial & Management Optimization","volume":"3 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114899499","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}
Many traditional retailers become multi-channel retailers by establishing self-operated online channel or employing e-retailer's e-marketplace, and some multi-channel retailers adopt price self-matching to mitigate intense price competition in multi-channel retailing. Our goal in this research is to examine how the multi-channel retailer's online channel design interacts with its price self-matching strategy in a supply chain including a multi-channel retailer and an e-retailer. Our study demonstrates that adopting price self-matching does not necessarily benefit the multi-channel retailer. Moreover, price self-matching can greatly impact the performance of the multi-channel retailer's online channel design, for example, under some market conditions where the multi-channel retailer can benefit from price self-matching only if it employs the e-retailer's e-marketplace, the multi-channel retailer should design online channel according to the e-marketplace's commission rate; but under other market conditions, it should always establish self-operated online channel. Overall, only the strategy of establishing self-operated online channel and adopting price self-matching and the strategy of employing the e-retailer's e-marketplace and adopting price self-matching can help the two retailers achieve a win-win situation. Furthermore, we show that, interestingly, a more prominent disadvantage of the self-operated online channel's potential demand benefits not only the e-retailer but also the multi-channel retailer.
{"title":"Online channel design in the presence of price self-matching: Self-operating or e-marketplace?","authors":"Jie Wei, Mei Ying Chang","doi":"10.3934/jimo.2022043","DOIUrl":"https://doi.org/10.3934/jimo.2022043","url":null,"abstract":"Many traditional retailers become multi-channel retailers by establishing self-operated online channel or employing e-retailer's e-marketplace, and some multi-channel retailers adopt price self-matching to mitigate intense price competition in multi-channel retailing. Our goal in this research is to examine how the multi-channel retailer's online channel design interacts with its price self-matching strategy in a supply chain including a multi-channel retailer and an e-retailer. Our study demonstrates that adopting price self-matching does not necessarily benefit the multi-channel retailer. Moreover, price self-matching can greatly impact the performance of the multi-channel retailer's online channel design, for example, under some market conditions where the multi-channel retailer can benefit from price self-matching only if it employs the e-retailer's e-marketplace, the multi-channel retailer should design online channel according to the e-marketplace's commission rate; but under other market conditions, it should always establish self-operated online channel. Overall, only the strategy of establishing self-operated online channel and adopting price self-matching and the strategy of employing the e-retailer's e-marketplace and adopting price self-matching can help the two retailers achieve a win-win situation. Furthermore, we show that, interestingly, a more prominent disadvantage of the self-operated online channel's potential demand benefits not only the e-retailer but also the multi-channel retailer.","PeriodicalId":347719,"journal":{"name":"Journal of Industrial & Management Optimization","volume":"60 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134593041","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}
Rumor is a kind of abnormal information, which spreads faster than normal information, and has high transmission intensity. The existing rumor spreading formulas give an explanation of rumor spreading intensity. However, there has been a lack of corresponding research on how to measure. This paper presents a method. Firstly, the rumor spreading formula is combed and commented, and the important influencing factors in the process of rumor spreading are extracted. Secondly, the influencing factors of rumor information dissemination are analyzed, and an uncertain evaluation index list of network rumor intensity is constructed, and the dissemination intensity of rumor information is measured based on uncertain comprehensive evaluation. Finally, the effectiveness of the application of the evaluation model is verified by a numerical example, and operational policy suggestions are given according to the analysis of the results.
{"title":"Uncertain comprehensive evaluation of the spreading intensity of internet rumors in the new media era","authors":"Chunhua Gao, Yufu Ning, Fengming Liu, Meiling Jin","doi":"10.3934/jimo.2022037","DOIUrl":"https://doi.org/10.3934/jimo.2022037","url":null,"abstract":"Rumor is a kind of abnormal information, which spreads faster than normal information, and has high transmission intensity. The existing rumor spreading formulas give an explanation of rumor spreading intensity. However, there has been a lack of corresponding research on how to measure. This paper presents a method. Firstly, the rumor spreading formula is combed and commented, and the important influencing factors in the process of rumor spreading are extracted. Secondly, the influencing factors of rumor information dissemination are analyzed, and an uncertain evaluation index list of network rumor intensity is constructed, and the dissemination intensity of rumor information is measured based on uncertain comprehensive evaluation. Finally, the effectiveness of the application of the evaluation model is verified by a numerical example, and operational policy suggestions are given according to the analysis of the results.","PeriodicalId":347719,"journal":{"name":"Journal of Industrial & Management Optimization","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133087316","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}
In this paper, we investigate the pricing of a path-dependent option with default risk under the Hawkes jump diffusion process. For each asset, its dynamics are driven by a Hawkes jump diffusion process, and their diffusive components, Hawkes jumps as well as jump amplitudes are all correlated. In the proposed pricing framework, we obtain the prices of fader options with/without default risk in closed form. Finally, we present numerical examples to illustrate the prices of fader options with default risk.
{"title":"Pricing path-dependent options under the Hawkes jump diffusion process","authors":"Xingchun Wang","doi":"10.3934/jimo.2022024","DOIUrl":"https://doi.org/10.3934/jimo.2022024","url":null,"abstract":"In this paper, we investigate the pricing of a path-dependent option with default risk under the Hawkes jump diffusion process. For each asset, its dynamics are driven by a Hawkes jump diffusion process, and their diffusive components, Hawkes jumps as well as jump amplitudes are all correlated. In the proposed pricing framework, we obtain the prices of fader options with/without default risk in closed form. Finally, we present numerical examples to illustrate the prices of fader options with default risk.","PeriodicalId":347719,"journal":{"name":"Journal of Industrial & Management Optimization","volume":"782 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"113996214","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}
Efficiency evaluation is a very important and key issue in competitive conditions. Organizations and companies face various uncertainties, and this makes it extremely difficult and complex to evaluate their efficiency. In this research, opened-network data envelopment analysis models have been developed in uncertain space for three uncertain states, including: uncertain outputs, uncertain inputs, and simultaneous uncertain inputs and outputs. The proposed models have been used to evaluate the efficiency of 10 two-stage processes, seller and buyer in a supply chain, and the impact of data uncertainty is examined. The results obtained from the developed models have been compared with the results of traditional DEA network models. The validity and accuracy of the developed models have also been examined. The results have shown that the reliability of the proposed models is higher than the traditional DEA network model. Also, by examining the efficiency of decision-making units in different conditions of data uncertainty and deviations, it was determined that the greater the range of this deviation, the lower the efficiency score of different units will be, which is consistent with reality.
{"title":"Development of opened-network data envelopment analysis models under uncertainty","authors":"H. Hosseini-Nasab, V. Ettehadi","doi":"10.3934/jimo.2022027","DOIUrl":"https://doi.org/10.3934/jimo.2022027","url":null,"abstract":"Efficiency evaluation is a very important and key issue in competitive conditions. Organizations and companies face various uncertainties, and this makes it extremely difficult and complex to evaluate their efficiency. In this research, opened-network data envelopment analysis models have been developed in uncertain space for three uncertain states, including: uncertain outputs, uncertain inputs, and simultaneous uncertain inputs and outputs. The proposed models have been used to evaluate the efficiency of 10 two-stage processes, seller and buyer in a supply chain, and the impact of data uncertainty is examined. The results obtained from the developed models have been compared with the results of traditional DEA network models. The validity and accuracy of the developed models have also been examined. The results have shown that the reliability of the proposed models is higher than the traditional DEA network model. Also, by examining the efficiency of decision-making units in different conditions of data uncertainty and deviations, it was determined that the greater the range of this deviation, the lower the efficiency score of different units will be, which is consistent with reality.","PeriodicalId":347719,"journal":{"name":"Journal of Industrial & Management Optimization","volume":"11 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117085771","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}
In this paper, we are concerned with the Galerkin spectral approximation of an optimal control problem governed by the Stokes equation with begin{document}$ L^2 $end{document}-norm constraint on the control variable. By means of the derived optimality conditions for both the original control system and its spectral approximation one, we establish a priori error estimates and then obtain a posteriori error estimator. A numerical example is, subsequently, executed to illustrate the effectiveness of method and the high performance of estimators. Furthermore, we conjecture that the similar conclusions should hold for optimal control of the Navier-Stokes equation. It is then confirmed by another numerical example.
In this paper, we are concerned with the Galerkin spectral approximation of an optimal control problem governed by the Stokes equation with begin{document}$ L^2 $end{document}-norm constraint on the control variable. By means of the derived optimality conditions for both the original control system and its spectral approximation one, we establish a priori error estimates and then obtain a posteriori error estimator. A numerical example is, subsequently, executed to illustrate the effectiveness of method and the high performance of estimators. Furthermore, we conjecture that the similar conclusions should hold for optimal control of the Navier-Stokes equation. It is then confirmed by another numerical example.
{"title":"Error estimates for spectral approximation of flow optimal control problem with $ L^2 $-norm control constraint","authors":"Zhenzhen Tao, Bing Sun","doi":"10.3934/jimo.2022030","DOIUrl":"https://doi.org/10.3934/jimo.2022030","url":null,"abstract":"<p style='text-indent:20px;'>In this paper, we are concerned with the Galerkin spectral approximation of an optimal control problem governed by the Stokes equation with <inline-formula><tex-math id=\"M2\">begin{document}$ L^2 $end{document}</tex-math></inline-formula>-norm constraint on the control variable. By means of the derived optimality conditions for both the original control system and its spectral approximation one, we establish a priori error estimates and then obtain a posteriori error estimator. A numerical example is, subsequently, executed to illustrate the effectiveness of method and the high performance of estimators. Furthermore, we conjecture that the similar conclusions should hold for optimal control of the Navier-Stokes equation. It is then confirmed by another numerical example.</p>","PeriodicalId":347719,"journal":{"name":"Journal of Industrial & Management Optimization","volume":"80 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122271119","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}
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