Optimum advertising policy over time for subscriber service innovations in the presence of service cost learning and customers’ disadoption

On the theoretical side, this paper characterizes qualitatively optimal advertising policy for new subscriber services. A monopolistic market is analyzed first for which customers’ disadoption, discounting of future profits streams and a service cost learning curve are allowed. After characterizing the optimal policy for a general diffusion model, the results pertaining to a specific diffusion model for which advertising affects the coefficient of innovation that incorporates the disadoption rate are reported. The results of the theoretical research show that the advertising policy of the service firm in the presence of customers’ disadoption could be very different from the same when disadoption is ignored.On the empirical side, four alternative diffusion models are estimated and their predictive powers using a one-step-ahead forecasting procedure compared. The diffusion data analyzed are related to the Canadian cable TV industry. Empirical research findings suggest that the specific diffusion model considered above is not only of theoretical appeal but also of major empirical relevance.The analytical findings of the study are documented in six theoretical propositions for which proofs are provided in a separate Appendix. The results of a related numerical experiment together with the analytical findings pertaining to the competitive role of advertising are included. Managerial implications of the study together with directions for future research are also discussed.     

Persistence and global stability of Bazykin predator–prey model with Beddington–DeAngelis response function

In this article, a predator–prey model of Beddington–DeAngelis type with discrete delay is proposed and analyzed. The essential mathematical features of the proposed model are investigated in terms of local, global analysis and bifurcation theory. By analyzing the associated characteristic equation, it is found that the Hopf bifurcation occurs when the delay parameter τ crosses some critical values. In this article, the classical Bazykin’s model is modified with Beddington–DeAngelis functional response. The parametric space under which the system enters into Hopf bifurcation for both delay and non-delay cases are investigated. Global stability results are obtained by constructing suitable Lyapunov functions for both the cases. We also derive the explicit formulae for determining the stability, direction and other properties of bifurcating periodic solutions by using normal form and central manifold theory. Our analytical findings are supported by numerical simulations. Biological implication of the analytical findings are discussed in the conclusion section.     

Effect of time-delay on a food chain model

This paper aims to study the effect of discrete time-delay on a tritrophic food chain model with Holling type-II functional responses. Dynamical behaviours such as boundedness, stability, persistence and bifurcation of the model are studied. Our analytical findings are illustrated through computer simulation. Biological implications of our analytical findings are addressed critically.     

Deterministic and stochastic analysis of a delayed allelopathic phytoplankton model within fluctuating environment

In this paper, we consider a two-dimensional model for two competitive phytoplankton species where one species is toxic phytoplankton and other is non-toxic species. The logistic growth of both the species follows the Hutchinson type growth law. First, we briefly discuss basic dynamical properties of non-delayed and delayed model system within deterministic environment. Next we formulate the stochastic delay differential equation model system to study the effect of environmental driving forces on the dynamical behavior. We calculate population fluctuation intensity (variance) for both species by Fourier transform method. Numerical simulations are carried out to substantiate the analytical findings. Significant results of our analytical findings and their interpretations from ecological point of view are provided in concluding section.     

Dynamical analysis of a delayed ratio-dependent Holling-Tanner predator-prey model

In this paper, a delayed Holling-Tanner predator-prey model with ratio-dependent functional response is considered. It is proved that the model system is permanent under certain conditions. The local asymptotic stability and the Hopf-bifurcation results are discussed. Qualitative behaviour of the singularity (0,0) is explored by using a blow up transformation. Global asymptotic stability analysis of the positive equilibrium is carried out. Numerical simulations are presented for the support of our analytical findings.     

First stages of drop impact on a dry surface: asymptotic model

After impact of a viscous liquid drop on a dry wall surrounded by a gas, the drop surface is highly deformed, leading to the formation of an axisymmetrical lateral lamella along the wall. A local asymptotic model for the potential flow and unsteady boundary layer flow is developed to describe the lamella dynamics at early stages after impact. The second-order potential flow displaced by the unsteady boundary layer is taken into account. The lamella shape, its velocity and pressure are calculated with this model in parametrical forms. The three model parameters are evaluated here by fitting with recent experimental findings.     

第三方数据平台精准营销收费模式研究

第三方数据平台通过大数据分析技术为商家提供精准营销服务,本文研究了两个竞争商家通过同一个数据平台进行精准营销时,平台收费模式(费率佣金与按销量收费)对商家竞争以及平台与商家利润的影响。研究发现:1)费率佣金模式的绩效依赖于费率参数,在精准度高的情况下,它不能最大化平台与商家的利润。2)与费率佣金相比,按销量收费模式显著提高了商家的利润,并且平台与商家的利润都随费用参数的增加而增加。3)从收费模式选择的角度,精准度越高,按销量收费模式的优势越明显;费率佣金模式适用于垄断情况,而按销量收费模式更适用于竞争情况。4)费率佣金与按销量收费的结合可以实现平台与商家的共赢。研究结论为大数据驱动下的精准营销收费模式选择,以及“大数据平台”的盈利模式创新提供了理论参考。     

Analysis of a spatially extended nonlinear SEIS epidemic model with distinct incidence for exposed and infectives

We present a nonlinear SEIS epidemic model which incorporates distinct incidence rates for the exposed and the infected populations. The model is analyzed for stability and bifurcation behavior. To account for the realistic phenomenon of non-homogeneous mixing, the effect of diffusion on different population subclasses is considered. The diffusive model is analyzed using matrix stability theory and conditions for Turing bifurcation derived. Numerical simulations are performed to justify analytical findings.     

Stochastic persistence and stability analysis of a modified Holling–Tanner model

The article aims to study the basic dynamical features of a modified Holling–Tanner prey–predator model with ratio‐dependent functional response. We have proved the global existence of the solution for the deterministic model. The parametric restriction for persistence of both species is also obtained along with the proof of local asymptotic stability of the interior equilibrium point(s). Conditions for local bifurcations of interior equilibrium points are provided. The global dynamic behavior is examined thoroughly with supportive numerical simulation results. Next, we have formulated the stochastic model by perturbing the intrinsic growth rates of prey and predator populations with white noise terms. The existence uniqueness of solutions for stochastic model is established. Further, we have derived the parametric restrictions required for the persistence of the stochastic model. Finally, we have discussed the stochastic stability results in terms of the first and second order moments. Numerical simulation results are provided to support the analytical findings. Copyright © 2012 John Wiley & Sons, Ltd.     

聚合物时温等效模型有限元应用研究

为更好地描述聚合物材料力学性能的温度相关性问题,对目前广泛应用的WLF模型进行改进研究,并引入“零时间”因子提高了粘弹性材料变温松弛模量的获取精度.在此基础上基于ABAQUS用户材料子程序UTRS将时温等效模型应用到数值计算中.根据不同温度水平下的应力松弛实验获得模型参数,并通过等速拉伸实验与数值结果的对比验证了该模型及其有限元方法的可行性及正确性.结果表明:引入“零时间”因子的变温松弛模量精度更高;改进WLF模型对复合推进剂具有更好的适用性和更高的精确度.     

On the molecular mechanisms driving pain perception and emergent collective behaviors

A stochastic model to investigate the microscopic processes which trigger the sensation of pain is considered. The model, presented in Di Patti and Fanelli [Di Patti F, Fanelli D. Can a microscopic stochastic model explain the emergence of pain cycles in patients? J Stat Mech 2009. doi:10.1088/1742-5468/2009/01/P01004], accounts for the action of analgesic drug and introduces an effect of competition with the inactive species populating the bloodstream. Regular oscillations in the amount of bound receptors are detected, following a resonant amplification of the stochastic component intrinsic to the system. The condition for such oscillations to occur are here studied, resorting to combined numerical and analytical techniques. Extended and connected patches of the admissible parameters space are detected which do correspond to the oscillatory behaviors. These findings are discussed with reference to the existing literature on patients’ response to the analgesic treatment.     

Towards hybrid two-phase modelling using linear domain decomposition

The viscous flow of two immiscible fluids in a porous medium on the Darcy scale is governed by a system of nonlinear parabolic equations. If infinite mobility of one phase can be assumed (e.g., in soil layers in contact with the atmosphere) the system can be substituted by the scalar Richards model. Thus, the porous medium domain may be partitioned into disjoint subdomains where either the full two-phase or the simplified Richards model dynamics are valid. Extending the previously considered one-model situations we suggest coupling conditions for this hybrid model approach. Based on an Euler implicit discretization, a linear iterative (L-type) domain decomposition scheme is proposed, and proved to be convergent. The theoretical findings are verified by a comparative numerical study that in particular confirms the efficiency of the hybrid ansatz as compared to full two-phase model computations.     

Investigation of a Phase Field Model for Elasto-plastic Fracture

Phase field modelling of brittle fracture is very well understood today. However, the attempts of investigation of elasto-plastic fracture by the phase field approach are limited. This contribution deals with the investigation of a phase field model for elasto-plastic fracture. Based on a free energy density comprising elastic, fracture and plastic contributions, the model describes an extension of the linear elastic model towards von Mises plasticity. In this work it is analyzed numerically to which extend analytical findings concerning the interpretation of the model parameters in 1D are transferable to 2D scenarios. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

基于线上评论的生鲜产品供应链定价策略

随着网络购物的普及,线上评论对消费者的购买决策发挥着越来越重要的作用,零售商和制造商可以利用这些评论调整、优化生产流程。本文基于消费者效用理论,构建了由一个零售商和一个制造商组成的生鲜产品供应链定价决策模型,研究了三种决策模式下生鲜产品零售价、利润和保鲜努力水平的差异。研究发现:集中决策下生鲜产品的最优零售价最低、利润最高;随着运输时间增加,保鲜努力水平和新鲜度均呈现下降趋势;当成本分担系数较高时,在成本分担和收益共享的分散决策模式下,保鲜努力最优水平高于集中决策模式下保鲜努力最优水平。     

Filter‐based portfolio strategies in an HMM setting with varying correlation parametrizations

We consider portfolio optimization in a regime‐switching market. The assets of the portfolio are modeled through a hidden Markov model (HMM) in discrete time, where drift and volatility of the single assets are allowed to switch between different states. We consider different parametrizations of the involved asset covariances: statewise uncorrelated assets (though linked through the common Markov chain), assets correlated in a state‐independent way, and assets where the correlation varies from state to state. As a benchmark, we also consider a model without regime switches. We utilize a filter‐based expectation‐maximization (EM) algorithm to obtain optimal parameter estimates within this multivariate HMM and present parameter estimators in all three HMM settings. We discuss the impact of these different models on the performance of several portfolio strategies. Our findings show that for simulated returns, our strategies in many settings outperform naïve investment strategies, like the equal weights strategy. Information criteria can be used to detect the best model for estimation as well as for portfolio optimization. A second study using real data confirms these findings.     

Stage-structured Harvest Models

We formulate a stage-structured population model where the population is divided to two classes, the juveniles and the adults. Then, we include harvest in the model and assume that the harvesting is only on adults. The cases where the harvesting rate is constant, proportional to the amount of adults, or of Holling-II type are studied. While the model dynamics are relatively simple when the harvesting rate is proportional, the model system with a constant or a Holling-II type harvesting rate can have multiple positive equilibria. We explore the existence of all possible equilibria and investigate their stability. We also give numerical examples to confirm our findings.     

Dynamics of an SIR epidemic model with limited medical resources revisited

The dynamics of an SIR epidemic model is explored in this paper in order to understand how the limited medical resources and their supply efficiency affect the transmission of infectious diseases. The study reveals that, with varying amount of medical resources and their supply efficiency, the target model admits both backward bifurcation and Hopf bifurcation. Sufficient criteria are established for the existence of backward bifurcation, the existence, the stability and the direction of Hopf bifurcation. The mechanism of backward bifurcation and its implication for the control of the infectious disease are also explored. Numerical simulations are presented to support and complement the theoretical findings.     

Bayesian modelling of the time delay between diagnosis and settlement for Critical Illness Insurance using a Burr generalised-linear-type model

We discuss Bayesian modelling of the delay between dates of diagnosis and settlement of claims in Critical Illness Insurance using a Burr distribution. The data are supplied by the UK Continuous Mortality Investigation and relate to claims settled in the years 1999-2005. There are non-recorded dates of diagnosis and settlement and these are included in the analysis as missing values using their posterior predictive distribution and MCMC methodology. The possible factors affecting the delay (age, sex, smoker status, policy type, benefit amount, etc.) are investigated under a Bayesian approach. A 3-parameter Burr generalised-linear-type model is fitted, where the covariates are linked to the mean of the distribution. Variable selection using Bayesian methodology to obtain the best model with different prior distribution setups for the parameters is also applied. In particular, Gibbs variable selection methods are considered, and results are confirmed using exact marginal likelihood findings and related Laplace approximations. For comparison purposes, a lognormal model is also considered.     

Confidence ellipsoids based on a general family of shrinkage estimators for a linear model with non-spherical disturbances

This paper considers a general family of Stein rule estimators for the coefficient vector of a linear regression model with nonspherical disturbances, and derives estimators for the Mean Squared Error (MSE) matrix, and risk under quadratic loss for this family of estimators. The confidence ellipsoids for the coefficient vector based on this family of estimators are proposed, and the performance of the confidence ellipsoids under the criterion of coverage probability and expected volumes is investigated. The results of a numerical simulation are presented to illustrate the theoretical findings, which could be applicable in the area of economic growth modeling.     

Robust equilibrium reinsurance-investment strategy for a mean–variance insurer in a model with jumps

This paper analyzes the equilibrium strategy of a robust optimal reinsurance-investment problem under the mean–variance criterion in a model with jumps for an ambiguity-averse insurer (AAI) who worries about model uncertainty. The AAI’s surplus process is assumed to follow the classical Cramér–Lundberg model, and the AAI is allowed to purchase proportional reinsurance or acquire new business and invest in a financial market to manage her risk. The financial market consists of a risk-free asset and a risky asset whose price process is described by a jump-diffusion model. By applying stochastic control theory, we establish the corresponding extended Hamilton–Jacobi–Bellman (HJB) system of equations. Furthermore, we derive both the robust equilibrium reinsurance-investment strategy and the corresponding equilibrium value function by solving the extended HJB system of equations. In addition, some special cases of our model are provided, which show that our model and results extend some existing ones in the literature. Finally, the economic implications of our findings are illustrated, and utility losses from ignoring model uncertainty, jump risks and prohibiting reinsurance are analyzed using numerical examples.