The Gaussian approximation for generalized Friedman’s urn model with heterogeneous and unbalanced updating

The Friedman’s urn model is a popular urn model which is widely used in many disciplines.In particular,it is extensively used in treatment allocation schemes in clinical trials.Its asymptotic properties have been studied by many researchers.In literature,it is usually assumed that the expected number of balls added at each stage is a constant in despite of what type of balls are selected,that is,the updating of the urn is assumed to be balanced.When it is not,the asymptotic property of the Friedman’s urn model is stated in the book of Hu and Rosenberger(2006) as one of open problems in the area of adaptive designs.In this paper,we show that both the urn composition process and the allocation proportion process can be approximated by a multi-dimensional Gaussian process almost surely for a general multi-color Friedman type urn model with heterogeneous and unbalanced updating.The Gaussian process is a solution of a stochastic differential equation.As an application,we obtain the asymptotic properties including the asymptotic normality and the exact law of the iterated logarithm.     

OPTIMAL PROPORTIONAL REINSURANCE AND INVESTMENT FOR A CONSTANT ELASTICITY OF VARIANCE MODEL UNDER VARIANCE PRINCIPLE

This article studies the optimal proportional reinsurance and investment problem under a constant elasticity of variance(CEV) model.Assume that the insurer’s surplus process follows a jump-diffusion process,the insurer can purchase proportional reinsurance from the reinsurer via the variance principle and invest in a risk-free asset and a risky asset whose price is modeled by a CEV model.The diffusion term can explain the uncertainty associated with the surplus of the insurer or the additional small claims.The objective of the insurer is to maximize the expected exponential utility of terminal wealth.This optimization problem is studied in two cases depending on the diffusion term’s explanation.In all cases,by using techniques of stochastic control theory,closed-form expressions for the value functions and optimal strategies are obtained.     

Revisit of the Faddeev Model in Dimension Two

The Faddeev model is a fundamental model in relativistic quantum ?eld theory used to model elementary particles. The Faddeev model can be regarded as a system of non-linear wave equations with both quasi-linear and semi-linear non-linearities, which is particularly challenging in two space dimensions. A key feature of the system is that there exist undi?erentiated wave components in the non-linearities, which somehow causes extra di?culties. Nevertheless, the Cauchy problem in two space dimenions was tackled by Lei-Lin-Zhou (2011) with small, regular, and compactly supported initial data, using Klainerman’s vector ?eld method enhanced by a novel angular-radial anisotropic technique. In the present paper, the authors revisit the Faddeev model and remove the compactness assumptions on the initial data by Lei-Lin-Zhou (2011). The proof relies on an improved L2 norm estimate of the wave components in Theorem 3.1 and a decomposition technique for non-linearities of divergence form.     

Empirical likelihood based goodness-of-fit testing for generalized linear mixed models

In this paper, we propose a bias-corrected empirical likelihood （BCEL） ratio to construct a goodness- of-fit test for generalized linear mixed models. BCEL test maintains the advantage of empirical likelihood that is self scale invariant and then does not involve estimating limiting variance of the test statistic to avoid deteri- orating power of test. Furthermore, the bias correction makes the limit to be a process in which every variable is standard chi-squared. This simple structure of the process enables us to construct a Monte Carlo test proce- dure to approximate the null distribution. Thus, it overcomes a problem we encounter when classical empirical likelihood test is used, as it is asymptotically a functional of Gaussian process plus a normal shift function. The complicated covariance function makes it difficult to employ any approximation for the null distribution. The test is omnibus and power study shows that the test can detect local alternatives approaching the null at parametric rate. Simulations are carried out for illustration and for a comparison with existing method.     

Time-consistent investment-reinsurance strategies towards joint interests of the insurer and the reinsurer under CEV models

The present paper studies time-consistent solutions to an investment-reinsurance problem under a mean-variance framework.The paper is distinguished from other literature by taking into account the interests of both an insurer and a reinsurer jointly.The claim process of the insurer is governed by a Brownian motion with a drift.A proportional reinsurance treaty is considered and the premium is calculated according to the expected value principle.Both the insurer and the reinsurer are assumed to invest in a risky asset,which is distinct for each other and driven by a constant elasticity of variance model.The optimal decision is formulated on a weighted sum of the insurer’s and the reinsurer’s surplus processes.Upon a verification theorem,which is established with a formal proof for a more general problem,explicit solutions are obtained for the proposed investment-reinsurance model.Moreover,numerous mathematical analysis and numerical examples are provided to demonstrate those derived results as well as the economic implications behind.     

The fast method and convergence analysis of the fractional magnetohydrodynamic coupled flow and heat transfer model for the generalized second-grade fluid

In this paper, we first establish a new fractional magnetohydrodynamic(MHD) coupled flow and heat transfer model for a generalized second-grade fluid. This coupled model consists of a fractional momentum equation and a heat conduction equation with a generalized form of Fourier law. The second-order fractional backward difference formula is applied to the temporal discretization and the Legendre spectral method is used for the spatial discretization. The fully discrete scheme is proved to be sta...     

Study on the model of an insurer’s solvency ratio in Markov-modulated Brownian markets

In this paper the insurer’s solvency ratio model with or without jump diffusion process in the presence of financial distress cost is constructed, where an insurer’s solvency ratio is characterized by a Markov-modulated dynamics. By Girsanov’s theorem and the option pricing formula, the expected present value of shareholders’ terminal payoff is provided.     

Dynamic optimal strategy for monitoring disease recurrence

Surveillance to detect cancer recurrence is an important part of care for cancer survivors.In this paper we discuss the design of optimal strategies for early detection of disease recurrence based on each patient’s distinct biomarker trajectory and periodically updated risk estimated in the setting of a prospective cohort study.We adopt a latent class joint model which considers a longitudinal biomarker process and an event process jointly,to address heterogeneity of patients and disease,to discover distinct biomarker trajectory patterns,to classify patients into different risk groups,and to predict the risk of disease recurrence.The model is used to develop a monitoring strategy that dynamically modifies the monitoring intervals according to patients’ current risk derived from periodically updated biomarker measurements and other indicators of disease spread.The optimal biomarker assessment time is derived using a utility function.We develop an algorithm to apply the proposed strategy to monitoring of new patients after initial treatment.We illustrate the models and the derivation of the optimal strategy using simulated data from monitoring prostate cancer recurrence over a 5-year period.     

具有内生基础设施分配的城市经济增长模型

In this paper, an urban economic growth model with endogenous infrastructure allocation is given by introducing the two-variable utility function for city＇s inhabitant. A twodimensional dynamical system is obtained by solving the utility maximization problem and it is proved that this system has the unique non-zero equilibrium which is a saddle. The model has the unique optimal growth and an optimal rate of infrastructure allocation.     

A proximal point algorithm revisit on the alternating direction method of multipliers

The alternating direction method of multipliers(ADMM)is a benchmark for solving convex programming problems with separable objective functions and linear constraints.In the literature it has been illustrated as an application of the proximal point algorithm(PPA)to the dual problem of the model under consideration.This paper shows that ADMM can also be regarded as an application of PPA to the primal model with a customized choice of the proximal parameter.This primal illustration of ADMM is thus complemental to its dual illustration in the literature.This PPA revisit on ADMM from the primal perspective also enables us to recover the generalized ADMM proposed by Eckstein and Bertsekas easily.A worst-case O(1/t)convergence rate in ergodic sense is established for a slight extension of Eckstein and Bertsekas’s generalized ADMM.     

Modeling and targeting an essential metabolic pathway of Plasmodium falciparum in apicoplast using Petri nets

Petri net(PN) is one of the promising computational and mathematical formalisms used to represent and study the behavior of complex metabolic networks. The various available analysis techniques of PN could be used to validate and analyze the network in different scenarios. Plasmodium falciparum is one of the threatening parasites which causes malaria, a deadly disease affecting a large number of today’s world population. The development of antimalarial drug resistance is an emerging global threat, highlighting the need to discover novel antimalarial targets. The fatty acid biosynthesis of malarial parasite is one of the essential metabolic pathways required for its growth and is present in apicoplast, a non-photosynthetic plastid. The malarial parasite obtains fatty acids by using type two fatty acid synthase(FAS II) enzyme,which is different from type one enzyme used by human host, making it an ideal drug target.This article proposes and studies the PN model of the parasite’s FAS II pathway to analyze the mechanism of potential drug targets in this pathway. The proposed PN model can serve as a base for further findings in the field of antimalarial drug targets to decrease the malaria mortality rate.     

PREFERENCE AND EVOLUTION IN THE ITERATED PRISONER＇S DILEMMA

Game theory is extensively used to study strategy-making and actions of play- ers. The authors proposed an analysis method for study the evolutionary outcome and behaviors of players with preference in iterated prisoner＇s dilemma. In this article, a preference parameter k was introduced in the payoff matrix, wherein the value of k denotes the player＇s degree of egoism and altruism （preference）. Then, a game-theoretic dynamical model was formulated using Birth-and-Death process. The authors studied how preference influences the evolutionary equilibrium and behaviors of players. The authors get the general results： egoism leads to defection, and altruism can make players build trust and maintain cooperation, and so, the hope of the Pareto optimal solution. In the end, the simulation experiments proved the efficiency of the method.     

MQ拟插值求解KdV方程

Quasi-interpolation is very useful in the study of approximation theory and its applications,since it can yield solutions directly without the need to solve any linear system of equations.Based on the good performance,Chen and Wu presented a kind of multiquadric （MQ） quasi-interpolation,which is generalized from the L D operator,and used it to solve hyperbolic conservation laws and Burgers’ equation.In this paper,a numerical scheme is presented based on Chen and Wu’s method for solving the Korteweg-de Vries （KdV） equation.The presented scheme is obtained by using the second-order central divided difference of the spatial derivative to approximate the third-order spatial derivative,and the forward divided difference to approximate the temporal derivative,where the spatial derivative is approximated by the derivative of the generalized L D quasi-interpolation operator.The algorithm is very simple and easy to implement and the numerical experiments show that it is feasible and valid.     

Survival probability and ruin probability of a risk model

In this paper, a new risk model is studied in which the rate of premium income is regarded as a random variable, the arrival of insurance policies is a Poisson process and the process of claim occurring is p-thinning process. The integral representations of the survival probability are gotten. The explicit formula of the survival probability on the infinite interval is obtained in the special casc cxponential distribution.The Lundberg inequality and the common formula of the ruin probability are gotten in terms of some techniques from martingale theory.     

Scale and time effects on mathematical models for transport in the environment

The purpose of this paper is to analyse mathematical models used in environmental modelling.Following a brief survey of the development in modelling scale-and time-dependent dispersion processes in the environment,this paper compares three similarity solutions,one of which is a solution of the generalized Feller equation(GF)with fractal parameters,and the other two for the newly-developed generalized Fokker-Planck equation(GFP).The three solutions are derived with parameters having physical significance.Data from field experiments are used to verify the solutions.The analyses indicate that the solutions of both GF and GFP represent the physically meaningful natural processes,and simulate the realistic shapes of tracer breakthrough curves.     

Classical Risk Model with Threshold Dividend Strategy

In this article, a threshold dividend strategy is used for classical risk model. Under this dividend strategy, certain probability of ruin, which occurs in case of constant barrier strategy, is avoided. Using the strong Markov property of the surplus process and the distribution of the deficit in classical risk model, the survival probability for this model is derived, which is more direct than that in Asmussen（2000, P195, Proposition 1.10）. The occupation time of non-dividend of this model is also discussed by means of Martingale method.     

A Penalty Approach for Generalized Nash Equilibrium Problem

The generalized Nash equilibrium problem (GNEP) is a generalization of the standard Nash equilibrium problem (NEP),in which both the utility function and the strategy space of each player depend on the strategies chosen by all other players.This problem has been used to model various problems in applications.However,the convergent solution algorithms are extremely scare in the literature.In this paper,we present an incremental penalty method for the GNEP,and show that a solution of the GNEP can be found by solving a sequence of smooth NEPs.We then apply the semismooth Newton method with Armijo line search to solve latter problems and provide some results of numerical experiments to illustrate the proposed approach.     

Generalized empirical likelihood inference in semiparametric regression model for longitudinal data

In this paper, we consider the semiparametric regression model for longitudinal data. Due to the correlation within groups, a generalized empirical log-likelihood ratio statistic for the unknown parameters in the model is suggested by introducing the working covariance matrix. It is proved that the proposed statistic is asymptotically standard chi-squared under some suitable conditions, and hence it can be used to construct the confidence regions of the parameters. A simulation study is conducted to compare the proposed method with the generalized least squares method in terms of coverage accuracy and average lengths of the confidence intervals.     

Flows associated to Cameron-Martin type vector fields on path spaces over a Riemannian manifold

The flow on the Wiener space associated to a tangent process constructed by Cipriano and Cruzeiro, as well as by Gong and Zhang does not allow to recover Driver’s Cameron-Martin theorem on Riemannian path space. The purpose of this work is to refine the method of the modified Picard iteration used in the previous work by Gong and Zhang and to try to recapture and extend the result of Driver. In this paper, we establish the existence and uniqueness of a flow associated to a Cameron-Martin type vector field on the path space over a Riemannian manifold.