A Note on the Mean-Variance Criteria for Discrete Time Financial Markets

It was shown in Xia that for incomplete markets with continuous assets＇ price processes and for complete markets the mean-variance portfolio selection can be viewed as expected utility maximization with non-negative marginal utility. In this paper we show that for discrete time incomplete markets this result is not true.     

具有不同效用函数的最优投资组合分析

The question of optimal portfolio is that finds the trading strategy satisfying the maximal expected utility function subject to some constraints. There is the optimal trading strategy under the risk neutral probability measure (martingale measure) if and only if there is no-arbitrage opportunity in the market. This paper argues the optimal wealth and the optimal value of expected utility with different utility function.     

Structure condition under initial enlargement of filtration

We address the question of how the structure condition is affected when one possesses some additional information at the very beginning of the investment period.The structure condition represents essentially an alternative to non-arbitrage conditions for the Markowitz’s portfolio optimization framework,and is crucial for the existence of the optimal portfolio in quadratic utility settings.Herein,we provide practical assumption on the initial market model and the additional information to preserve the structure condition.The stochastic tools that drive this result are a generalization of the Lazaro-Yor representation by Lazaro and Yor(1978)and optional stochastic integral.     

The Ruin Probability in the Presence of Extended Regular Variation and Optimal Investment

Considering the classical model with risky investment, we are interested in the ruin probability that is minimized by a suitably chosen investment strategy for a capital market index. For claim sizes with common distribution of extended regular variation, starting from an integro-differential equation for the maximal survival probability, we find that the corresponding ruin probability as a function of the initial surplus is also extended regular variation.     

带非局部阻尼项的粘弹性方程解的衰减估计

In this paper,we consider the following viscoelastic equation u tt- △u +∫t 0 g(t-s)△u(s)ds + a(x)u t + u |u|r = 0 with initial condition and Dirichlet boundary condition.The decay property of the energy function closely depends on the properties of the relaxation function g(t) at infinity.In the previous works of [3,7,11],it was required that the relaxation function g(t) decay exponentially or polynomially as t → +∞.In the recent work of Messaoudi [12,13],it was shown that the energy decays at a similar rate of decay of the relaxation function,which is not necessarily dacaying in a polynomial or exponential fashion.Motivated by [12,13],under some assumptions on g(x),a(x) and r,and by introducing a new perturbed energy,we also prove the similar results for the above equation.     

EXTINCTION OF A DISCRETE NONLINEAR PREDATOR-PREY SYSTEM

In this paper, we consider a discrete nonlinear predator-prey model with nonnegative coefficients bounded above and below by positive constants. We show that under some suitable assumptions the predator species is driven to extinction and the prey species x is globally attractive with any positive solution to a discrete Logistic equation.     

Smoothness of certain functions in two kinds of risk models with a barrier dividend strategy

In this paper,we study the smoothness of certain functions in two kinds of risk models with a barrier dividend strategy.Mainly using technique from the piecewise deterministic Markov processes theory,we prove that the function is continuously differentiable in the first risk model.Using the weak infinitesimal generator method of Markov processes,we prove that the function is twice continuously differentiable in the second risk model.Intego-differential equations satisfied by them are derived.     

PERMANENCE AND GLOBAL STABILITY OF POSITIVE SOLUTIONS TO TWO PREDATORSONE PREY SYSTEM WITH A DISCRETE TIME RATIO-DEPENDENT

A three-species ratio-dependent predator-prey discrete model is studied.As a result,sufficient conditions which guarantee the permanence of the model are obtained. In addition,by constructing a suitable Lyapunov function,we derive some sufficient conditions,which ensure that the positive solution of the model is stable and attracts all positive solutions.To illustrate the feasibility of the main results,we introduce an example with corresponding numeric simulations.     

STUDY ON THE INTERRELATION OF EFFICIENT PORTFOLIOS AND THEIR FRONTIER UNDER t DISTRIBUTION AND VARIOUS RISK MEASURES

In order to study the effect of different risk measures on the efficient portfolios (frontier) while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivari-ate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios (frontier) based on risk measures such as variance, value at risk (VaR), and expected shortfall (ES) is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance (MV) efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.     

CONVERGENCE RATES TO TRAVELLING WAVES FOR A RELAXATION MODEL WITH LARGE INITIAL DISTURBANCE

This paper is concerned with the convergence rates to traveUmg waves for a relaxation model with general flux functions. Compared with former results in thisdirection, the main novelty in this paper lies in the fact that the initial disturbance can bechosen large in suitable norm. Our analysis is based on the L^1-stability results obtainedby C. Macia and R. Natalini in [12].     

STUDY ON THE INTERRELATION OF EFFICIENT PORTFOLIOS AND THEIR FRONTIER UNDER t DISTRIBUTION AND VARIOUS RISK MEASUREgS

In order to study the effect of different risk measures on the efficient portfolios （fron- tier） while properly describing the characteristic of return distributions in the stock market, it is assumed in this paper that the joint return distribution of risky assets obeys the multivariate t-distribution. Under the mean-risk analysis framework, the interrelationship of efficient portfolios （frontier） based on risk measures such as variance, value at risk （VaR）, and expected shortfall （ES） is analyzed and compared. It is proved that, when there is no riskless asset in the market, the efficient frontier under VaR or ES is a subset of the mean-variance （MV） efficient frontier, and the efficient portfolios under VaR or ES are also MV efficient; when there exists a riskless asset in the market, a portfolio is MV efficient if and only if it is a VaR or ES efficient portfolio. The obtained results generalize relevant conclusions about investment theory, and can better guide investors to make their investment decision.     

具有时滞和毒素系统的动力学分析

In this paper, a toxin producing phytoplankton-zooplankton model with inhibitory substrate and time delay is investigated. A discrete time delay is induced to both of the consume response function and distribution of toxic substance term. Moreover, Tissiet type function is used for zooplankton grazing to account for the effect of toxication by the TPP population. The conditions to guarantee the coexistence of two species and stability of coexistence equilibrium are given. In particular, we show that there exist critical values of the delay parameters below which the coexistence equilibrium is stable and above which it is unstable. Hopf bifurcation occurs when the delay parameters cross their critical values. Some numerical simulations are executed to validate the analytical findings.     

GLOBAL NONEXISTENCE FOR A VISCOELASTIC WAVE EQUATION WITH ACOUSTIC BOUNDARY CONDITIONS

This paper deals with a class of nonlinear viscoelastic wave equation with damping and source terms ■ with acoustic boundary conditions. Under some appropriate assumption on relaxation function g and the initial data, we prove that the solution blows up in finite time if the positive initial energy satisfies a suitable condition.     

Dynamic asset allocation with loss aversion in a jump-diffusion model

This paper investigates a dynamic asset allocation problem for loss-averse investors in a jumpdiffusion model where there are a riskless asset and N risky assets. Specifically, the prices of risky assets are governed by jump-diffusion processes driven by an m-dimensional Brownian motion and a(N- m)-dimensional Poisson process. After converting the dynamic optimal portfolio problem to a static optimization problem in the terminal wealth, the optimal terminal wealth is first solved. Then the optimal wealth process and investment strategy are derived by using the martingale representation approach. The closed-form solutions for them are finally given in a special example.     

EXISTENCE OF OPTIMAL POLICY FOR TIME NON-HOMOGENEOUS DISCOUNTED MARKOVIAN DECISION PR0GRAMMING

In this paper we discuss the discrete, time non--homogeneous discounted Markovian decisionprogramming, where the state space and all action sets are countable. Suppose that the optimumvalue function is finite. We give the necessary and sufficient conditions for the existence of anoptimal policy. Suppose that the absolute mean of rewards is relatively bounded. We also give thenecessary and sufficient conditions for the existence of an optimal policy.     

Irregular wavelet frames on L~2 (R~n)

In this paper, we present the conditions on dilation parameter {sj}j that ensure a discrete irregular wavelet system to be a frame on L2(Rn), and for the wavelet frame we consider the perturbations of translation parameter b and frame function ψ respectively.     

IMPACT OF OPERATING COSTS ON INVESTMENT STRATEGIES IN NEW TECHNOLOGY ADOPTION WITH A FURTHER NEW TECHNOLOGY ANTICIPATED

The adoption of new technologies often represents a crucial component of firms＇ investment decisions. This paper studies a dynamic duopoly model in which two firms compete in adoption of current technology with a further new technology anticipated. Here it is assumed that the operating costs are not zero which has more explanatory power of the real world. There exist three kinds of equilibria that may occur in adoption of current technology, which mainly depends on the level of operating costs and the first-move advantage. It shows that the faster technological substitution or innovation encourages the leader to invest earlier while induces the follower to invest later. Furthermore,like the investment costs,with the increase of operating costs the follower tends to invest later while the leader tends to invest earlier ,the investment thresholds are more sensitive to the change of operating costs than that of investment costs.     

非线性比式和问题的全局优化算法

In this paper,a global optimization algorithm is proposed for nonlinear sum of ratios problem(P).The algorithm works by globally solving problem(P1) that is equivalent to problem(P),by utilizing linearization technique a linear relaxation programming of the (P1) is then obtained.The proposed algorithm is convergent to the global minimum of(P1) through the successive refinement of linear relaxation of the feasible region of objective function and solutions of a series of linear relaxation programming.Nume...     

PERMANENCE OF A SIRS EPIDEMIC MODEL WITH IMPULSIVE VACCINATION AND DISTRIBUTED DELAYS

In this paper, we consider a SIRS epidemic model with impulsive vaccination and distributed time delays. By the discrete dynamical system determined by the stroboscopic map, we obtain the exact infection-free periodic solution to the system. Further, using the comparison theorem, we prove that the infection-free periodic solution is globally attractive under an assumption. A sufficient condition for the permanence of the model is investigated.     

一类无约束离散Minimax问题的区间调节熵算法

In this paper,a class of unconstrained discrete minimax problems is described,in which the objective functions are in C^1. The paper deals with this problem by means of taking the place of maximum-entropy function with adjustable entropy function. By constructing an interval extension of adjustable entropy function and some region deletion test rules, a new interval algorithm is presented. The relevant properties are proven, The minimax value and the localization of the minimax points of the problem can be obtained by this method. This method can overcome the flow problem in the maximum-entropy algorithm. Both theoretical and numerical results show that the method is reliable and efficient.