Charge generation,a critical process in the operation of organic solar cell(OSC),requires thorough investigation in an ultrafast perspective.This work demonstrates that the utilization of alloy model for the non-fulle...Charge generation,a critical process in the operation of organic solar cell(OSC),requires thorough investigation in an ultrafast perspective.This work demonstrates that the utilization of alloy model for the non-fullerene acceptor(NFA)component can regulate the crystallization properties of active layer films,which in turn affects exciton diffusion and hole transfer(HT),ultimately influencing the charge generation process.By incorporating BTP-eC7 as a third component,without expanding absorption range or changing molecular energy levels but regulating the ultrafast exciton diffusion and HT processes,the power conversion efficiency(PCE)of the optimized PM6:BTP-eC9:BTP-eC7 based ternary OSC is improved from 17.30%to 17.83%,primarily due to the enhancement of short-circuit current density(JSC).Additionally,the introduction of BTP-eC7 also reduces the trap state density in the photoactive layer which helps to reduce the loss of JSC.This study introduces a novel approach for employing ternary alloy models by incorporating dual acceptors with similar structures,and elucidates the underlying mechanism of charge generation and JSC in ternary OSCs.展开更多
In this paper, we investigate a Sparre Andersen risk model perturbed by diffusion with phase-type inter-claim times. We mainly study the distribution of maximum surplus prior to ruin. A matrix form of integro-differen...In this paper, we investigate a Sparre Andersen risk model perturbed by diffusion with phase-type inter-claim times. We mainly study the distribution of maximum surplus prior to ruin. A matrix form of integro-differential equation for this quantity is derived, and its solution can be expressed as a linear combination of particular solutions of the corresponding homogeneous integro-differential equations. By using the divided differences technique and nonnegative real part roots of Lundberg＇s equation, the explicit Laplace transforms of particular solutions are obtained. Specially, we can deduce closed-form results as long as the individual claim size is rationally distributed. We also give a concise matrix expression for the expected discounted dividend payments under a barrier dividend strategy. Finally, we give some examples to present our main results.展开更多
This paper considers a perturbed renewal risk process in which the inter-claim times have a phasetype distribution under a threshold dividend strategy. Integro-differential equations with certain boundary conditions f...This paper considers a perturbed renewal risk process in which the inter-claim times have a phasetype distribution under a threshold dividend strategy. Integro-differential equations with certain boundary conditions for the moment-generating function and the ruth moment of the present value of all dividends until ruin are derived. Explicit expressions for the expectation of the present value of all dividends until ruin are obtained when the claim amount distribution is from the rational family. Finally, we present an example.展开更多
Nonlinear dynamical stochastic models are ubiquitous in different areas.Their statistical properties are often of great interest,but are also very challenging to compute.Many excitable media models belong to such type...Nonlinear dynamical stochastic models are ubiquitous in different areas.Their statistical properties are often of great interest,but are also very challenging to compute.Many excitable media models belong to such types of complex systems with large state dimensions and the associated covariance matrices have localized structures.In this article,a mathematical framework to understand the spatial localization for a large class of stochastically coupled nonlinear systems in high dimensions is developed.Rigorous mathematical analysis shows that the local effect from the diffusion results in an exponential decay of the components in the covariance matrix as a function of the distance while the global effect due to the mean field interaction synchronizes different components and contributes to a global covariance.The analysis is based on a comparison with an appropriate linear surrogate model,of which the covariance propagation can be computed explicitly.Two important applications of these theoretical results are discussed.They are the spatial averaging strategy for efficiently sampling the covariance matrix and the localization technique in data assimilation.Test examples of a linear model and a stochastically coupled Fitz Hugh-Nagumo model for excitable media are adopted to validate the theoretical results.The latter is also used for a systematical study of the spatial averaging strategy in efficiently sampling the covariance matrix in different dynamical regimes.展开更多
This paper studies the optimal dividend problem in the diffusion model with stochastic return on investments. The insurance company invests its surplus in a financial market. More specially, the authors consider the c...This paper studies the optimal dividend problem in the diffusion model with stochastic return on investments. The insurance company invests its surplus in a financial market. More specially, the authors consider the case of investment in a Black-Scholes market with risky asset such as stock. The classical problem is to find the optimal dividend payment strategy that maximizes the expectation of discounted dividend payment until ruin. Motivated by the idea of Thonhauser and Albrecher （2007）, we take the lifetime of the controlled risk process into account, that is, the value function considers both the expectation of discounted dividend payment and the time value of ruin. The authors conclude that the optimal dividend strategy is a barrier strategy for the unbounded dividend payment case and is of threshold type for the bounded dividend payment case.展开更多
This paper studies the first passage time problem for a reflected two-sided jump-diffusion risk model with the jumps having a hyper-Erlang distribution.The authors give the explicit closed-form expression for the join...This paper studies the first passage time problem for a reflected two-sided jump-diffusion risk model with the jumps having a hyper-Erlang distribution.The authors give the explicit closed-form expression for the joint Laplace transform of the first passage time and the overshoot for the reflected process.Finally,the formula is applied to the ruin problem under the barrier dividend strategy and the pricing of the Russian option.展开更多
基金supported by the National Natural Science Foundation of China(52073162)Major Program of Natural Science Foundation of Shandong Province(ZR2019ZD43)+1 种基金X.T.H also acknowledges support from the Taishan Scholars Program(tstp20230610)ARC Centre of Excellence in Exciton Science(CE170100026).
文摘Charge generation,a critical process in the operation of organic solar cell(OSC),requires thorough investigation in an ultrafast perspective.This work demonstrates that the utilization of alloy model for the non-fullerene acceptor(NFA)component can regulate the crystallization properties of active layer films,which in turn affects exciton diffusion and hole transfer(HT),ultimately influencing the charge generation process.By incorporating BTP-eC7 as a third component,without expanding absorption range or changing molecular energy levels but regulating the ultrafast exciton diffusion and HT processes,the power conversion efficiency(PCE)of the optimized PM6:BTP-eC9:BTP-eC7 based ternary OSC is improved from 17.30%to 17.83%,primarily due to the enhancement of short-circuit current density(JSC).Additionally,the introduction of BTP-eC7 also reduces the trap state density in the photoactive layer which helps to reduce the loss of JSC.This study introduces a novel approach for employing ternary alloy models by incorporating dual acceptors with similar structures,and elucidates the underlying mechanism of charge generation and JSC in ternary OSCs.
基金Supported by National Basic Research Program of China （973 Program） 2007CB814905, National Natural Science Foundation of China （Grant No. 10871102）, and the Keygrant Project of Chinese Ministry of Education （Grant No. 309009）
文摘In this paper, we investigate a Sparre Andersen risk model perturbed by diffusion with phase-type inter-claim times. We mainly study the distribution of maximum surplus prior to ruin. A matrix form of integro-differential equation for this quantity is derived, and its solution can be expressed as a linear combination of particular solutions of the corresponding homogeneous integro-differential equations. By using the divided differences technique and nonnegative real part roots of Lundberg＇s equation, the explicit Laplace transforms of particular solutions are obtained. Specially, we can deduce closed-form results as long as the individual claim size is rationally distributed. We also give a concise matrix expression for the expected discounted dividend payments under a barrier dividend strategy. Finally, we give some examples to present our main results.
基金Supported by the National Natural Sciences Foundations of China (70971037 and 71171078)the Doctoral Fund of Ministry of Education of China (20100161110022)+3 种基金China Postdoctoral Science Foundation funded project(2012M521514)Hunan Postdoctoral Scientific Program of China (2012RS4030)the Sciences Foundations of Hunan Institute of Science and Technology of China (2012Y26)the aid program for Science and Technology Research Team in Higher Educational Institutions of Hunan Province of China
文摘This paper considers a perturbed renewal risk process in which the inter-claim times have a phasetype distribution under a threshold dividend strategy. Integro-differential equations with certain boundary conditions for the moment-generating function and the ruth moment of the present value of all dividends until ruin are derived. Explicit expressions for the expectation of the present value of all dividends until ruin are obtained when the claim amount distribution is from the rational family. Finally, we present an example.
基金supported by the Office of Vice Chancellor for Research and Graduate Education(VCRGE)at University of Wisconsin-Madisonthe Office of Naval Research Grant ONR MURI N00014-16-1-2161+1 种基金the Center for Prototype Climate Modeling(CPCM)at New York University Abu Dhabi Research InstituteNUS Grant R-146-000-226-133
文摘Nonlinear dynamical stochastic models are ubiquitous in different areas.Their statistical properties are often of great interest,but are also very challenging to compute.Many excitable media models belong to such types of complex systems with large state dimensions and the associated covariance matrices have localized structures.In this article,a mathematical framework to understand the spatial localization for a large class of stochastically coupled nonlinear systems in high dimensions is developed.Rigorous mathematical analysis shows that the local effect from the diffusion results in an exponential decay of the components in the covariance matrix as a function of the distance while the global effect due to the mean field interaction synchronizes different components and contributes to a global covariance.The analysis is based on a comparison with an appropriate linear surrogate model,of which the covariance propagation can be computed explicitly.Two important applications of these theoretical results are discussed.They are the spatial averaging strategy for efficiently sampling the covariance matrix and the localization technique in data assimilation.Test examples of a linear model and a stochastically coupled Fitz Hugh-Nagumo model for excitable media are adopted to validate the theoretical results.The latter is also used for a systematical study of the spatial averaging strategy in efficiently sampling the covariance matrix in different dynamical regimes.
基金This work is supported by the National Basic Research Program of China （973 Program） under Grant No. 2007CB814905 and the National Natural Science Foundation of China under Grant No. 10871102.
文摘This paper studies the optimal dividend problem in the diffusion model with stochastic return on investments. The insurance company invests its surplus in a financial market. More specially, the authors consider the case of investment in a Black-Scholes market with risky asset such as stock. The classical problem is to find the optimal dividend payment strategy that maximizes the expectation of discounted dividend payment until ruin. Motivated by the idea of Thonhauser and Albrecher （2007）, we take the lifetime of the controlled risk process into account, that is, the value function considers both the expectation of discounted dividend payment and the time value of ruin. The authors conclude that the optimal dividend strategy is a barrier strategy for the unbounded dividend payment case and is of threshold type for the bounded dividend payment case.
基金supported by the Natural Science Foundation of China under Grant Nos.11301369,11401419the Natural Science Foundation of Jiangsu Province under Grant Nos.BK20130260,BK20140279
文摘This paper studies the first passage time problem for a reflected two-sided jump-diffusion risk model with the jumps having a hyper-Erlang distribution.The authors give the explicit closed-form expression for the joint Laplace transform of the first passage time and the overshoot for the reflected process.Finally,the formula is applied to the ruin problem under the barrier dividend strategy and the pricing of the Russian option.
