Leveraging energy harvesting abilities in wireless network devices has emerged as an effective way to prolong the lifetime of energy constrained systems.The system gains are usually optimized by designing resource all...Leveraging energy harvesting abilities in wireless network devices has emerged as an effective way to prolong the lifetime of energy constrained systems.The system gains are usually optimized by designing resource allocation algorithm appropriately.However,few works focus on the interaction that channel’s time-vary characters make the energy transfer inefficiently.To address this,we propose a novel system operation sequence for sensor-cloud system where the Sinks provide SWIPT for sensor nodes opportunistically during downlink phase and collect the data transmitted from sensor nodes in uplink phase.Then,the energy-efficiency maximization problem of the Sinks is presented by considering the time costs and energy consumption of channel detection.It is proved that the formulated problem is an optimal stopping process with optimal stopping rules.An optimal energy-efficiency(OEE)algorithm is designed to obtain the optimal stopping rules for SWIPT.Finally,the simulations are performed based on the OEE algorithm compared with the other two strategies to verify the effectiveness and gains in improving the system efficiency.展开更多
Background:In this paper,we study the right time for an investor to stop the investment over a given investment horizon so as to obtain as close to the highest possible wealth as possible,according to a Logarithmic ut...Background:In this paper,we study the right time for an investor to stop the investment over a given investment horizon so as to obtain as close to the highest possible wealth as possible,according to a Logarithmic utility-maximization objective involving the portfolio in the drift and volatility terms.The problem is formulated as an optimal stopping problem,although it is non-standard in the sense that the maximum wealth involved is not adapted to the information generated over time.Methods:By delicate stochastic analysis,the problem is converted to a standard optimal stopping one involving adapted processes.Results:Numerical examples shed light on the efficiency of the theoretical results.Conclusion:Our investment problem,which includes the portfolio in the drift and volatility terms of the dynamic systems,makes the problem including multi-dimensional financial assets more realistic and meaningful.展开更多
Convertible bond gives holder the right to choose a conversion strategy to maximize the bond value,and issuer also has the right to minimize the bond value in order to maximize equity value.When there is default occur...Convertible bond gives holder the right to choose a conversion strategy to maximize the bond value,and issuer also has the right to minimize the bond value in order to maximize equity value.When there is default occurring,conversion and calling strategies are invalid.In the framework of reduced form model,we reduce the price of convertible bond to variational inequalities,and the coefficients of variational inequalities are unbounded at the original point.Then the existence and uniqueness of variational inequality are proven.Finally,we prove that the conversion area,the calling area and the holding area are connected subsets of the state space.展开更多
Several factors influence bus transit reliability which includes bus stop conditions along the route, traffic conditions, route of travel and time of day. The overall transit bus reli- ability is generally affected by...Several factors influence bus transit reliability which includes bus stop conditions along the route, traffic conditions, route of travel and time of day. The overall transit bus reli- ability is generally affected by dwell time （DT）, the fare payment method, the bus stop location, and the number of passengers alighting or boarding. A new variable is defined in this study, total bus stop time （TBST）, which is the summation of DT and the time it takes a bus to effectively park at a bus stop and the re-entering the traffic stream. It is suggested that the overall bus transit reliability along routes could be improved if the TBST is mini- mized at bus stops. In this study, TBST models for bus stops located at mid-blocks and near intersections were developed based on multivariate regression analysis using ordinary least squares method. Data collection was conducted at 60 bus stops, 30 of which were near intersections and 30 at mid-blocks, in Washington DC during morning, mid-day and evening peak hours. The variables observed at each bus stop are as follows： number of passengers alighting or boarding, DT, TBST, bus stop type, bus pad, length number of lanes on approach to the bus stop, and permitted parking. Statistical inferences were based on 5% level of significance. From the results, it was inferred that the new variable, TBST, could potentially be used to improve scheduling and transit bus systems planning in a dense urban area.展开更多
This article develops a model to examine the equilibrium behavior of the time inconsistency problem in a continuous time economy with stochastic and endogenized distortion. First, the authors introduce the notion of s...This article develops a model to examine the equilibrium behavior of the time inconsistency problem in a continuous time economy with stochastic and endogenized distortion. First, the authors introduce the notion of sequentially rational equilibrium, and show that the time inconsistency problem may be solved with trigger reputation strategies for stochastic setting. The conditions for the existence of sequentially rational equilibrium are provided. Then, the concept of sequentially rational stochastically stable equilibrium is introduced. The authors compare the relative stability between the cooperative behavior and uncooperative behavior, and show that the cooperative equilibrium in this monetary policy game is a sequentially rational stochastically stable equilibrium and the uncooperative equilibrium is sequentially rational stochastically unstable equilibrium. In the long run, the zero inflation monetary policies are inherently more stable than the discretion rules, and once established, they tend to persist for longer periods of the time.展开更多
This paper deals with a secretary problem on fuzzy sets, which allows both the recall of applicants and the uncertainty of a current applicant receiving an offer of employmellt. A new decision criterion is given to se...This paper deals with a secretary problem on fuzzy sets, which allows both the recall of applicants and the uncertainty of a current applicant receiving an offer of employmellt. A new decision criterion is given to select a satisfactory applicant. This result extends the works of M.C.K. Yang and M.H. Smith.展开更多
Employee stock options （ESOs） have become an integral component of compensation in the US. In view of their significant cost to firms, the Financial Accounting Standards Board （FASB） has mandated expensing ESOs si...Employee stock options （ESOs） have become an integral component of compensation in the US. In view of their significant cost to firms, the Financial Accounting Standards Board （FASB） has mandated expensing ESOs since 2004. The main difficulty of ESO valuation lies in the uncertain timing of exercises, and a number of contractual restrictions of ESOs further complicate the problem. We present a valuation framework that captures the main characteristics of ESOs. Specifically, we incorporate the holder＇s risk aversion, and hedging strategies that include both dynamic trading of a correlated asset and static positions in market-traded options. Their combined effect on ESO exercises and costs are evaluated along with common features like vesting periods, job termination risk and multiple exercises. This leads to the study of a joint stochastic control and optimal stopping problem. We find that ESO values are much less than the corresponding Black-Scholes prices due to early exercises, which arise from risk aversion and job termination risk; whereas static hedges induce holders to delay exercises and increase ESO costs.展开更多
In this paper, by using the optimal stopping theory, the semilinear Black-Scholes partial differential equation （PDE） was invesigated in a fixed domain for valuing two assets of American （call-max/put-min） options...In this paper, by using the optimal stopping theory, the semilinear Black-Scholes partial differential equation （PDE） was invesigated in a fixed domain for valuing two assets of American （call-max/put-min） options. From the viscosity solution of a PDE, a unique viscosity solution was obtained for the semilinear Black-Scholes PDE.展开更多
In the research of choosing the optimal timing for the high technology products, especially IT products to the market, most studies prefer to provide the scope or infnnum of timing. In this paper, an optimal rule is a...In the research of choosing the optimal timing for the high technology products, especially IT products to the market, most studies prefer to provide the scope or infnnum of timing. In this paper, an optimal rule is adopted to guild the timing of high technology product to the market, this idea is illustrated through the theory of optimal stopping, and a high approach is developed to theoretical framework for timing decision. On this basis, a random programming model is established, in which the objective function is the expected profit to adopt high technology and the constraint condition is the successful probability over critical value a with all variables beyond the rule, and it is used to find the optimal timing of adopt high technology product.展开更多
We consider the optimal stopping time problem under model uncertainty,R(u)=ess supess sup EP[Y(↑)Fu],for every stopping time u,within the framework of families ofrandomevariables indexed by stopping times.This settin...We consider the optimal stopping time problem under model uncertainty,R(u)=ess supess sup EP[Y(↑)Fu],for every stopping time u,within the framework of families ofrandomevariables indexed by stopping times.This setting is more general than PEP TESU the classical setup of stochastic processes,notably allowing for general payoff processes that are not necessarily right-continuous.Under weaker integrability,with regularity assumptions for the reward family Y=(Y(u),u E S),the existence of an optimal stopping time is demonstrated.Sufficient conditions for the existence of an optimal model are then determined.For this purpose,we present a universal optional decomposition for the generalized Snell envelope family associated with Y.This decomposition is then employed to prove the existence of an optimal probability model and to study its properties.展开更多
In this study,we develop a theory of optimal stopping problems within the Gexpectation framework.To address this problem,we first introduce a type of random times.called G-stopping times,which are specifically suited ...In this study,we develop a theory of optimal stopping problems within the Gexpectation framework.To address this problem,we first introduce a type of random times.called G-stopping times,which are specifically suited for this setting.In the discrete-time case with a finite horizon,we define the value function backward and show that it is the smallest G-supermartingale that dominates the payoff process,ensuring the existence of an optimal stopping time.We then extend these results to both the infinite-horizon case and the continuous-time setting.Moreover,we establish the relationship between the value function and the solution of the reflected backward stochastic differential equation driven by G-Brownian motion.展开更多
With the wide application of Mobile Edge Computing(MEC)in the Internet of Vehicles and other fields,mobile nodes are no longer limited to smart phones,but also include new mobile devices such as smart vehicles.Faced w...With the wide application of Mobile Edge Computing(MEC)in the Internet of Vehicles and other fields,mobile nodes are no longer limited to smart phones,but also include new mobile devices such as smart vehicles.Faced with the access of a large number of devices,there may be situations where some edge servers are overloaded while others are relatively idle.To address this issue,a load aware multi-task offloading strategy based on optimal stopping theory is proposed,which minimizes the average load of the selected edge servers through sequential decisionmaking.Firstly,consider the cost of delaying decision-making and introduce a benefit function to constrain the number of observations.Secondly,the optimal stopping time is determined by solving the secretary problem with observation constraints.Finally,extending to the scenario of multi-task offloading,design a phased decision-making multi-task offloading algorithm.The simulation experiment results show that the proposed offloading strategy can significantly reduce the average load of the selected edge servers for task offloading,and can more effectively optimize the workload of edge servers.展开更多
In this paper, we discuss relations between optimal stopping problems over tree sets and partially ordered sets, prove that there is a 1-1 correspondence between them and so every optimal strategy can be obtained in t...In this paper, we discuss relations between optimal stopping problems over tree sets and partially ordered sets, prove that there is a 1-1 correspondence between them and so every optimal strategy can be obtained in the set of optimal control variables.展开更多
Relay selection for Relay Assisted(RA)networks is an economical and effective method to improve the spectrum efficiency.Relay selection performs especially well when the source node has accurate and timely Channel Sta...Relay selection for Relay Assisted(RA)networks is an economical and effective method to improve the spectrum efficiency.Relay selection performs especially well when the source node has accurate and timely Channel State Information(CSI).However,since perfect CSI knowledge is rarely available,research of relay selection with partial(statistical)CSI is of paramount importance.In this paper,relay selection for RA networks with statistical CSI is formulated as a Multiple-Decision(MD)problem.And,the cost of obtaining the CSI is also considered in the formulated problem.Two relay selection schemes,Maximal Selection Probability(MSP)and Maximal Spectrum Efficiency Expectation(MSEE),are proposed to solve the formulated MD problem under different optimal criteria assumptions based on the optimal stopping theory.The MSP scheme maximizes the probability that the Best Assisted Relay Candidate(BARC)can be selected,whereas the MSEE scheme provides the maximal expectation of the spectrum efficiency.Experimental results show that the proposed schemes effectively improve the spectrum efficiency,and the MSEE scheme is more suitable for stable communication cases.Meanwhile,the MSP scheme is more suitable for burst communication cases.展开更多
Software cybernetics explores the interplay between control theory/engineering and software theory/engineering. The controlled Markov chains (CMC) approach to software testing follows the idea of software cybernetics ...Software cybernetics explores the interplay between control theory/engineering and software theory/engineering. The controlled Markov chains (CMC) approach to software testing follows the idea of software cybernetics and treats software testing as a control problem. The software under test serves as a controlled object and the software testing strategy serves as the corresponding controller. The software under test and the software testing strategy make up a closed-loop feedback control system, and the theory of controlled Markov chains can be used to design and optimize software testing strategies in accordance with testing/reliability goals given a priori. In this paper we apply the CMC approach to the optimal stopping problem of multi-project software testing. The problem under consideration assumes that a single stopping action can stop testing of all the software systems under test simultaneously. The theoretical results presented in this paper describe how to test multiple software systems and when to stop testing in an optimal manner. An illustrative example is used to explain the theoretical results. The study of this paper further justifies the effectiveness of the CMC approach to software testing in particular and the idea of software cybernetics in general.展开更多
The author studies the optimal investment stopping problem in both continuous and discrete cases, where the investor needs to choose the optimal trading strategy and optimal stopping time concurrently to maximize the ...The author studies the optimal investment stopping problem in both continuous and discrete cases, where the investor needs to choose the optimal trading strategy and optimal stopping time concurrently to maximize the expected utility of terminal wealth.Based on the work of Hu et al.(2018) with an additional stochastic payoff function,the author characterizes the value function for the continuous problem via the theory of quadratic reflected backward stochastic differential equations(BSDEs for short) with unbounded terminal condition. In regard to the discrete problem, she gets the discretization form composed of piecewise quadratic BSDEs recursively under Markovian framework and the assumption of bounded obstacle, and provides some useful a priori estimates about the solutions with the help of an auxiliary forward-backward SDE system and Malliavin calculus. Finally, she obtains the uniform convergence and relevant rate from discretely to continuously quadratic reflected BSDE, which arise from corresponding optimal investment stopping problem through above characterization.展开更多
In this work,we study a right time for an investor to stop the investment among multi-assets over a given investment horizon so as to obtainmaximum profit.We formulate it to a two-stage problem.The main problem is not...In this work,we study a right time for an investor to stop the investment among multi-assets over a given investment horizon so as to obtainmaximum profit.We formulate it to a two-stage problem.The main problem is not a standard optimal stopping problem due to the non-adapted term in the objective function,and we turn it to a standard one by stochastic analysis.The subproblem with control variable in the drift and volatility terms is solved first via stochastic control method.A numerical example is presented to illustrate the efficiency of the theoretical results.展开更多
Given a continuous semimartingale M = （Mt）t≥〉0 and a d-dimensional continuous process of locally bounded variation V = （V^1,……, V^d）, the multidimensional Ito Formula states that f（Mt, Vt） - f（M0, V0） = ...Given a continuous semimartingale M = （Mt）t≥〉0 and a d-dimensional continuous process of locally bounded variation V = （V^1,……, V^d）, the multidimensional Ito Formula states that f（Mt, Vt） - f（M0, V0） = ∫[0, t] Dx0f（Ms, Vs）dMs＋∑i=1^d∫[0, t] Dxi F（Ms, Vs）dVs^i＋1/2∫[0, t] Dx0^2 f（Ms, Vs）d 〈M〉s if f（x0,……,xd） is of C^2-type with respect to x0 and of C^1-type with respect to the other arguments This formula is very useful when solving various optimal stopping problems based on Brownian motion. However, in such application the function f typically fails to satisfy the stated conditions in that its first partial derivative with respect to x0 is only absolutely continuous. We prove that the formula remains true for such functions and demonstrate its use with two examples from Mathematical Finance.展开更多
We show that“full-bang”control is optimal in a problem which combines features of(i)sequential least-squares estimation with Bayesian updating,for a random quantity observed in a bath of white noise;(ii)bounded cont...We show that“full-bang”control is optimal in a problem which combines features of(i)sequential least-squares estimation with Bayesian updating,for a random quantity observed in a bath of white noise;(ii)bounded control of the rate at which observations are received,with a superquadratic cost per unit time;and(iii)“fast”discretionary stopping.We develop also the optimal filtering and stopping rules in this context.展开更多
In this study,we delve into the optimal stopping problem by examining the p(ϕ(τ),τ∈T_(0)^(p))case in which the reward is given by a family of nonnegative random variables indexed by predictable stopping times.We ai...In this study,we delve into the optimal stopping problem by examining the p(ϕ(τ),τ∈T_(0)^(p))case in which the reward is given by a family of nonnegative random variables indexed by predictable stopping times.We aim to elucidate various properties of the value function family within this context.We prove the existence of an optimal predictable stopping time,subject to specific assumptions regarding the reward functionϕ.展开更多
基金This work was supported by Scientific Research Ability Improving Foundation for Young and Middle-Aged University Teachers in Guangxi(No.2020KY04030)The school introduces talents to start scientific research projects(No.2019KJQD17)+1 种基金This work was supported in part by the National Natural Science Foundation of China(No.61762010,No.61862007)Guangxi Natural Science Foundation(No.2018GXNSFAA138147).
文摘Leveraging energy harvesting abilities in wireless network devices has emerged as an effective way to prolong the lifetime of energy constrained systems.The system gains are usually optimized by designing resource allocation algorithm appropriately.However,few works focus on the interaction that channel’s time-vary characters make the energy transfer inefficiently.To address this,we propose a novel system operation sequence for sensor-cloud system where the Sinks provide SWIPT for sensor nodes opportunistically during downlink phase and collect the data transmitted from sensor nodes in uplink phase.Then,the energy-efficiency maximization problem of the Sinks is presented by considering the time costs and energy consumption of channel detection.It is proved that the formulated problem is an optimal stopping process with optimal stopping rules.An optimal energy-efficiency(OEE)algorithm is designed to obtain the optimal stopping rules for SWIPT.Finally,the simulations are performed based on the OEE algorithm compared with the other two strategies to verify the effectiveness and gains in improving the system efficiency.
基金This work is supported by Research Grants Council of Hong Kong under grant no.519913 and 15224215National Natural Science Foundation of China(No.11571124).
文摘Background:In this paper,we study the right time for an investor to stop the investment over a given investment horizon so as to obtain as close to the highest possible wealth as possible,according to a Logarithmic utility-maximization objective involving the portfolio in the drift and volatility terms.The problem is formulated as an optimal stopping problem,although it is non-standard in the sense that the maximum wealth involved is not adapted to the information generated over time.Methods:By delicate stochastic analysis,the problem is converted to a standard optimal stopping one involving adapted processes.Results:Numerical examples shed light on the efficiency of the theoretical results.Conclusion:Our investment problem,which includes the portfolio in the drift and volatility terms of the dynamic systems,makes the problem including multi-dimensional financial assets more realistic and meaningful.
基金Supported by the NNSF of China(10671144)NBRP of China(2007CB814903)
文摘Convertible bond gives holder the right to choose a conversion strategy to maximize the bond value,and issuer also has the right to minimize the bond value in order to maximize equity value.When there is default occurring,conversion and calling strategies are invalid.In the framework of reduced form model,we reduce the price of convertible bond to variational inequalities,and the coefficients of variational inequalities are unbounded at the original point.Then the existence and uniqueness of variational inequality are proven.Finally,we prove that the conversion area,the calling area and the holding area are connected subsets of the state space.
文摘Several factors influence bus transit reliability which includes bus stop conditions along the route, traffic conditions, route of travel and time of day. The overall transit bus reli- ability is generally affected by dwell time （DT）, the fare payment method, the bus stop location, and the number of passengers alighting or boarding. A new variable is defined in this study, total bus stop time （TBST）, which is the summation of DT and the time it takes a bus to effectively park at a bus stop and the re-entering the traffic stream. It is suggested that the overall bus transit reliability along routes could be improved if the TBST is mini- mized at bus stops. In this study, TBST models for bus stops located at mid-blocks and near intersections were developed based on multivariate regression analysis using ordinary least squares method. Data collection was conducted at 60 bus stops, 30 of which were near intersections and 30 at mid-blocks, in Washington DC during morning, mid-day and evening peak hours. The variables observed at each bus stop are as follows： number of passengers alighting or boarding, DT, TBST, bus stop type, bus pad, length number of lanes on approach to the bus stop, and permitted parking. Statistical inferences were based on 5% level of significance. From the results, it was inferred that the new variable, TBST, could potentially be used to improve scheduling and transit bus systems planning in a dense urban area.
基金the National Natural Science Foundation of China (70602012),Texas Advanced Research Program as well as from the Bush Program in the Economics of Public Policy,the Private Enterprise Research Center, and the Lewis Faculty Fellowship at Texas A & M University
文摘This article develops a model to examine the equilibrium behavior of the time inconsistency problem in a continuous time economy with stochastic and endogenized distortion. First, the authors introduce the notion of sequentially rational equilibrium, and show that the time inconsistency problem may be solved with trigger reputation strategies for stochastic setting. The conditions for the existence of sequentially rational equilibrium are provided. Then, the concept of sequentially rational stochastically stable equilibrium is introduced. The authors compare the relative stability between the cooperative behavior and uncooperative behavior, and show that the cooperative equilibrium in this monetary policy game is a sequentially rational stochastically stable equilibrium and the uncooperative equilibrium is sequentially rational stochastically unstable equilibrium. In the long run, the zero inflation monetary policies are inherently more stable than the discretion rules, and once established, they tend to persist for longer periods of the time.
文摘This paper deals with a secretary problem on fuzzy sets, which allows both the recall of applicants and the uncertainty of a current applicant receiving an offer of employmellt. A new decision criterion is given to select a satisfactory applicant. This result extends the works of M.C.K. Yang and M.H. Smith.
文摘Employee stock options （ESOs） have become an integral component of compensation in the US. In view of their significant cost to firms, the Financial Accounting Standards Board （FASB） has mandated expensing ESOs since 2004. The main difficulty of ESO valuation lies in the uncertain timing of exercises, and a number of contractual restrictions of ESOs further complicate the problem. We present a valuation framework that captures the main characteristics of ESOs. Specifically, we incorporate the holder＇s risk aversion, and hedging strategies that include both dynamic trading of a correlated asset and static positions in market-traded options. Their combined effect on ESO exercises and costs are evaluated along with common features like vesting periods, job termination risk and multiple exercises. This leads to the study of a joint stochastic control and optimal stopping problem. We find that ESO values are much less than the corresponding Black-Scholes prices due to early exercises, which arise from risk aversion and job termination risk; whereas static hedges induce holders to delay exercises and increase ESO costs.
基金Project supported by the National Natural Science Foundation of China (Grant No.10271072)
文摘In this paper, by using the optimal stopping theory, the semilinear Black-Scholes partial differential equation （PDE） was invesigated in a fixed domain for valuing two assets of American （call-max/put-min） options. From the viscosity solution of a PDE, a unique viscosity solution was obtained for the semilinear Black-Scholes PDE.
文摘In the research of choosing the optimal timing for the high technology products, especially IT products to the market, most studies prefer to provide the scope or infnnum of timing. In this paper, an optimal rule is adopted to guild the timing of high technology product to the market, this idea is illustrated through the theory of optimal stopping, and a high approach is developed to theoretical framework for timing decision. On this basis, a random programming model is established, in which the objective function is the expected profit to adopt high technology and the constraint condition is the successful probability over critical value a with all variables beyond the rule, and it is used to find the optimal timing of adopt high technology product.
文摘We consider the optimal stopping time problem under model uncertainty,R(u)=ess supess sup EP[Y(↑)Fu],for every stopping time u,within the framework of families ofrandomevariables indexed by stopping times.This setting is more general than PEP TESU the classical setup of stochastic processes,notably allowing for general payoff processes that are not necessarily right-continuous.Under weaker integrability,with regularity assumptions for the reward family Y=(Y(u),u E S),the existence of an optimal stopping time is demonstrated.Sufficient conditions for the existence of an optimal model are then determined.For this purpose,we present a universal optional decomposition for the generalized Snell envelope family associated with Y.This decomposition is then employed to prove the existence of an optimal probability model and to study its properties.
基金supported by the Natural Science Foundation of Shandong Province for Excellent Young Scientists Fund Program(Overseas)(Grant No.2023HWYQ-049)the National Natural Science Foundation of China(Grant No.12301178)+1 种基金the Natural Science Foundation of Shandong Province(Grant No.ZR2022QA022)the Fundamental ResearchFundsfor the Central Universities.
文摘In this study,we develop a theory of optimal stopping problems within the Gexpectation framework.To address this problem,we first introduce a type of random times.called G-stopping times,which are specifically suited for this setting.In the discrete-time case with a finite horizon,we define the value function backward and show that it is the smallest G-supermartingale that dominates the payoff process,ensuring the existence of an optimal stopping time.We then extend these results to both the infinite-horizon case and the continuous-time setting.Moreover,we establish the relationship between the value function and the solution of the reflected backward stochastic differential equation driven by G-Brownian motion.
基金supported in part by the National Natural Science Foundation of China(Nos.6206207 and 62472300)Guangxi Natural Science Foundation(No.2025GXNSFAA069236)Guangxi Key R&D Program(No.2024AB33144).
文摘With the wide application of Mobile Edge Computing(MEC)in the Internet of Vehicles and other fields,mobile nodes are no longer limited to smart phones,but also include new mobile devices such as smart vehicles.Faced with the access of a large number of devices,there may be situations where some edge servers are overloaded while others are relatively idle.To address this issue,a load aware multi-task offloading strategy based on optimal stopping theory is proposed,which minimizes the average load of the selected edge servers through sequential decisionmaking.Firstly,consider the cost of delaying decision-making and introduce a benefit function to constrain the number of observations.Secondly,the optimal stopping time is determined by solving the secretary problem with observation constraints.Finally,extending to the scenario of multi-task offloading,design a phased decision-making multi-task offloading algorithm.The simulation experiment results show that the proposed offloading strategy can significantly reduce the average load of the selected edge servers for task offloading,and can more effectively optimize the workload of edge servers.
文摘In this paper, we discuss relations between optimal stopping problems over tree sets and partially ordered sets, prove that there is a 1-1 correspondence between them and so every optimal strategy can be obtained in the set of optimal control variables.
基金supported by the National Natural Science Foundation of Shaanxi Province (Nos.2018JM6075 and2018JM6098)Shaanxi Key Laboratory of Integrated and Intelligent Navigation Open Fund (No.SKLIIN20180211)the Research Foundation for Talented Scholars of Xijing University (Nos.XJ19B01 and XJ17B06)
文摘Relay selection for Relay Assisted(RA)networks is an economical and effective method to improve the spectrum efficiency.Relay selection performs especially well when the source node has accurate and timely Channel State Information(CSI).However,since perfect CSI knowledge is rarely available,research of relay selection with partial(statistical)CSI is of paramount importance.In this paper,relay selection for RA networks with statistical CSI is formulated as a Multiple-Decision(MD)problem.And,the cost of obtaining the CSI is also considered in the formulated problem.Two relay selection schemes,Maximal Selection Probability(MSP)and Maximal Spectrum Efficiency Expectation(MSEE),are proposed to solve the formulated MD problem under different optimal criteria assumptions based on the optimal stopping theory.The MSP scheme maximizes the probability that the Best Assisted Relay Candidate(BARC)can be selected,whereas the MSEE scheme provides the maximal expectation of the spectrum efficiency.Experimental results show that the proposed schemes effectively improve the spectrum efficiency,and the MSEE scheme is more suitable for stable communication cases.Meanwhile,the MSP scheme is more suitable for burst communication cases.
基金supported by the National Outstanding Youth Foundation of China,the"863"Programme of China and the Aviation Science Foundation of China.
文摘Software cybernetics explores the interplay between control theory/engineering and software theory/engineering. The controlled Markov chains (CMC) approach to software testing follows the idea of software cybernetics and treats software testing as a control problem. The software under test serves as a controlled object and the software testing strategy serves as the corresponding controller. The software under test and the software testing strategy make up a closed-loop feedback control system, and the theory of controlled Markov chains can be used to design and optimize software testing strategies in accordance with testing/reliability goals given a priori. In this paper we apply the CMC approach to the optimal stopping problem of multi-project software testing. The problem under consideration assumes that a single stopping action can stop testing of all the software systems under test simultaneously. The theoretical results presented in this paper describe how to test multiple software systems and when to stop testing in an optimal manner. An illustrative example is used to explain the theoretical results. The study of this paper further justifies the effectiveness of the CMC approach to software testing in particular and the idea of software cybernetics in general.
基金This work was supported by the China Scholarship Councilthe National Science Foundation of China(No.11631004)the Science and Technology Commission of Shanghai Municipality(No.14XD1400400)。
文摘The author studies the optimal investment stopping problem in both continuous and discrete cases, where the investor needs to choose the optimal trading strategy and optimal stopping time concurrently to maximize the expected utility of terminal wealth.Based on the work of Hu et al.(2018) with an additional stochastic payoff function,the author characterizes the value function for the continuous problem via the theory of quadratic reflected backward stochastic differential equations(BSDEs for short) with unbounded terminal condition. In regard to the discrete problem, she gets the discretization form composed of piecewise quadratic BSDEs recursively under Markovian framework and the assumption of bounded obstacle, and provides some useful a priori estimates about the solutions with the help of an auxiliary forward-backward SDE system and Malliavin calculus. Finally, she obtains the uniform convergence and relevant rate from discretely to continuously quadratic reflected BSDE, which arise from corresponding optimal investment stopping problem through above characterization.
基金This work is supported by the National Natural Science Foundation of China(Nos.11571124 and 11671158)the doctoral start-up Grant of Natural Science Foundation of Guangdong Province,China(No.2017A030310167)the Opening Project of Guangdong Province Key Laboratory of Computational Science at the Sun Yat-sen University(No.201808)and Unversity of Macao(No.MYGR2018-00047-FST).
文摘In this work,we study a right time for an investor to stop the investment among multi-assets over a given investment horizon so as to obtainmaximum profit.We formulate it to a two-stage problem.The main problem is not a standard optimal stopping problem due to the non-adapted term in the objective function,and we turn it to a standard one by stochastic analysis.The subproblem with control variable in the drift and volatility terms is solved first via stochastic control method.A numerical example is presented to illustrate the efficiency of the theoretical results.
基金Partially supported by the Deutsche Forschungsgemeinschaft(DFG) under Grant SCHM 677/7-1
文摘Given a continuous semimartingale M = （Mt）t≥〉0 and a d-dimensional continuous process of locally bounded variation V = （V^1,……, V^d）, the multidimensional Ito Formula states that f（Mt, Vt） - f（M0, V0） = ∫[0, t] Dx0f（Ms, Vs）dMs＋∑i=1^d∫[0, t] Dxi F（Ms, Vs）dVs^i＋1/2∫[0, t] Dx0^2 f（Ms, Vs）d 〈M〉s if f（x0,……,xd） is of C^2-type with respect to x0 and of C^1-type with respect to the other arguments This formula is very useful when solving various optimal stopping problems based on Brownian motion. However, in such application the function f typically fails to satisfy the stated conditions in that its first partial derivative with respect to x0 is only absolutely continuous. We prove that the formula remains true for such functions and demonstrate its use with two examples from Mathematical Finance.
基金Erik Ekström acknowledges the support from the Swedish Research Council(Grant No.2019-03525)Ioannis Karatzas acknowledges the support from the National Science Foundation(Grant No.NSF-DMS-20-04977).
文摘We show that“full-bang”control is optimal in a problem which combines features of(i)sequential least-squares estimation with Bayesian updating,for a random quantity observed in a bath of white noise;(ii)bounded control of the rate at which observations are received,with a superquadratic cost per unit time;and(iii)“fast”discretionary stopping.We develop also the optimal filtering and stopping rules in this context.
文摘In this study,we delve into the optimal stopping problem by examining the p(ϕ(τ),τ∈T_(0)^(p))case in which the reward is given by a family of nonnegative random variables indexed by predictable stopping times.We aim to elucidate various properties of the value function family within this context.We prove the existence of an optimal predictable stopping time,subject to specific assumptions regarding the reward functionϕ.
