We study the Nadaraya-Watson estimators for the drift function of two-sided reflected stochastic differential equations.The estimates,based on either the continuously observed process or the discretely observed proces...We study the Nadaraya-Watson estimators for the drift function of two-sided reflected stochastic differential equations.The estimates,based on either the continuously observed process or the discretely observed process,are considered.Under certain conditions,we prove the strong consistency and the asymptotic normality of the two estimators.Our method is also suitable for one-sided reflected stochastic differential equations.Simulation results demonstrate that the performance of our estimator is superior to that of the estimator proposed by Cholaquidis et al.(Stat Sin,2021,31:29-51).Several real data sets of the currency exchange rate are used to illustrate our proposed methodology.展开更多
In this paper, the evaluation of discretely sampled Asian options was considered by numerically solving the associated partial differential equations with the Legendre spectral method. Double average options were disc...In this paper, the evaluation of discretely sampled Asian options was considered by numerically solving the associated partial differential equations with the Legendre spectral method. Double average options were discussed as examples. The problem is a parabolic one on a finite domain whose equation degenerates into ordinary differential equations on the boundaries. A fully discrete scheme was established by using the Legendre spectral method in space and the Crank-Nicolson finite difference scheme in time. The stability and convergence of the scheme were analyzed. Numerical results show that the method can keep the spectral accuracy in space for such degenerate problems.展开更多
We study the quantitative stability of solutions to Markovian quadratic reflected backward stochastic differential equations(BSDEs)with bounded terminal data.By virtue of bounded mean oscillation martingale and change...We study the quantitative stability of solutions to Markovian quadratic reflected backward stochastic differential equations(BSDEs)with bounded terminal data.By virtue of bounded mean oscillation martingale and change of measure techniques,we obtain stability estimates for the variation of the solutions with different underlying forward processes.In addition,we propose a truncated discrete-time numerical scheme for quadratic reflected BSDEs and obtain the explicit rate of convergence by applying the quantitative stability result.展开更多
Job-shop scheduling problem with discretely controllable processing times (JSP-DCPT) is modeled based on the disjunctive graph, and the formulation of JSP-DCPT is presented. A three-step decomposition approach is prop...Job-shop scheduling problem with discretely controllable processing times (JSP-DCPT) is modeled based on the disjunctive graph, and the formulation of JSP-DCPT is presented. A three-step decomposition approach is proposed so that JSP-DCPT can be handled by solving a job-shop scheduling problem (JSP) and a series of discrete time-cost tradeoff problems. To simplify the decomposition approach, the time-cost phase plane is introduced to describe tradeoffs of the discrete time-cost tradeoff problem, and an extreme mode-based set dominant theory is elaborated so that an upper bound is determined to cut discrete time-cost tradeoff problems generated by using the proposed decomposition approach. An extreme mode-based set dominant decomposition algorithm (EMSDDA) is then proposed. Experimental simulations for instance JSPDCPT_FT10, which is designed based on a JSP benchmark FT10, demonstrate the effectiveness of the proposed theory and the decomposition approach.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
Non-planar morphology is a common feature of devices applied in various physical fields,such as light or fluid,which pose a great challenge for surface nano-patterning to improve their performance.The present study pr...Non-planar morphology is a common feature of devices applied in various physical fields,such as light or fluid,which pose a great challenge for surface nano-patterning to improve their performance.The present study proposes a discretely-supported nanoimprint.lithography(NIL)technique to fabricate nanostructures on the extremely non-planar surface,namely high-spatial-frequency stepped surface.The designed discretely imprinting template implanted a discretely-supported intermediate buffer layer made of sparse pillars arrays.This allowed the simultaneous generation of air-cushion-like buffer and reliable support to the thin structured layer in the template.The resulting low bending stiffness and distributed concentrated load of the template jointly overcome the contact difficulty with a stepped surface,and enable the template to encase the stepped protrusion as tight as possible.Based on the proposed discretely-supported NIL,nanostructures were fabricated on the luminous interface of light emitting diodes chips that covered with micrometer step electrodes pad.About 96%of the utilized indium tin oxide transparent current spreading layer surface on top of the light emitting diode(LED)chips was coated with nanoholes array,with an increase by more than 40%in the optical output power.The excellent ability of nanopatterning a non-planar substrate could potentially lead innovate design and development of high performance device based on discretely-supported NIL.展开更多
基金partially supported by the National Natural Science Foundation of China(11871244)the Fundamental Research Funds for the Central Universities,JLU。
文摘We study the Nadaraya-Watson estimators for the drift function of two-sided reflected stochastic differential equations.The estimates,based on either the continuously observed process or the discretely observed process,are considered.Under certain conditions,we prove the strong consistency and the asymptotic normality of the two estimators.Our method is also suitable for one-sided reflected stochastic differential equations.Simulation results demonstrate that the performance of our estimator is superior to that of the estimator proposed by Cholaquidis et al.(Stat Sin,2021,31:29-51).Several real data sets of the currency exchange rate are used to illustrate our proposed methodology.
文摘In this paper, the evaluation of discretely sampled Asian options was considered by numerically solving the associated partial differential equations with the Legendre spectral method. Double average options were discussed as examples. The problem is a parabolic one on a finite domain whose equation degenerates into ordinary differential equations on the boundaries. A fully discrete scheme was established by using the Legendre spectral method in space and the Crank-Nicolson finite difference scheme in time. The stability and convergence of the scheme were analyzed. Numerical results show that the method can keep the spectral accuracy in space for such degenerate problems.
基金supported by China Scholarship Council.Gechun Liang is partially supported by the National Natural Science Foundation of China(Grant No.12171169)Guangdong Basic and Applied Basic Research Foundation(Grant No.2019A1515011338)+1 种基金GL thanks J.F.Chassagneux and A.Richou for helpful and inspiring discussions on how to extend to the state dependent volatility case.Shanjian Tang is partially supported by National Science Foundation of China(Grant No.11631004)National Key R&D Program of China(Grant No.2018YFA0703903).
文摘We study the quantitative stability of solutions to Markovian quadratic reflected backward stochastic differential equations(BSDEs)with bounded terminal data.By virtue of bounded mean oscillation martingale and change of measure techniques,we obtain stability estimates for the variation of the solutions with different underlying forward processes.In addition,we propose a truncated discrete-time numerical scheme for quadratic reflected BSDEs and obtain the explicit rate of convergence by applying the quantitative stability result.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51075337, 50705076, 50705077)the Natural Sci-ence Basic Research Plan in Shaanxi Province of China (Grant No. 2009JQ9002)
文摘Job-shop scheduling problem with discretely controllable processing times (JSP-DCPT) is modeled based on the disjunctive graph, and the formulation of JSP-DCPT is presented. A three-step decomposition approach is proposed so that JSP-DCPT can be handled by solving a job-shop scheduling problem (JSP) and a series of discrete time-cost tradeoff problems. To simplify the decomposition approach, the time-cost phase plane is introduced to describe tradeoffs of the discrete time-cost tradeoff problem, and an extreme mode-based set dominant theory is elaborated so that an upper bound is determined to cut discrete time-cost tradeoff problems generated by using the proposed decomposition approach. An extreme mode-based set dominant decomposition algorithm (EMSDDA) is then proposed. Experimental simulations for instance JSPDCPT_FT10, which is designed based on a JSP benchmark FT10, demonstrate the effectiveness of the proposed theory and the decomposition approach.
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financed by the National Key R&D Program of China(No.2017YFB1102900)the Natural Science Foundation of China(No.51805422)+1 种基金the China Postdoctoral Science Foundation(No.2019M653592)the Basic Research Program of Natural Science of Shaanxi Province of China(No.2019JLM-5).
文摘Non-planar morphology is a common feature of devices applied in various physical fields,such as light or fluid,which pose a great challenge for surface nano-patterning to improve their performance.The present study proposes a discretely-supported nanoimprint.lithography(NIL)technique to fabricate nanostructures on the extremely non-planar surface,namely high-spatial-frequency stepped surface.The designed discretely imprinting template implanted a discretely-supported intermediate buffer layer made of sparse pillars arrays.This allowed the simultaneous generation of air-cushion-like buffer and reliable support to the thin structured layer in the template.The resulting low bending stiffness and distributed concentrated load of the template jointly overcome the contact difficulty with a stepped surface,and enable the template to encase the stepped protrusion as tight as possible.Based on the proposed discretely-supported NIL,nanostructures were fabricated on the luminous interface of light emitting diodes chips that covered with micrometer step electrodes pad.About 96%of the utilized indium tin oxide transparent current spreading layer surface on top of the light emitting diode(LED)chips was coated with nanoholes array,with an increase by more than 40%in the optical output power.The excellent ability of nanopatterning a non-planar substrate could potentially lead innovate design and development of high performance device based on discretely-supported NIL.
