基于mean-variance的服务集群负载均衡方法

大量并发请求任务进行分配时,负载调度机制是通过最小化响应时间及最大化节点利用率实现网络中节点的负载均衡,在基于遗传算法的负载均衡算法中,适应度函数设计对服务集群负载均衡效率产生重要的影响。对此提出了一种基于mean-variance的服务集群负载均衡方法对适应度函数进行优化,采用投资组合选择模型mean-variance进行最小化响应时间,以得到每个服务器资源利用率的权重,从而获得最优的分配组合,进而提高适应度函数的准确性和有效性。在不同服务环境下与其他模型进行比较,仿真结果表明,本文的负载均衡算法在节点利用率和响应时间方面使服务集群得到了更好的均衡。

MARKOV-MODULATED MEAN-VARIANCE PROBLEM FOR AN INSURER

In this paper, we consider an insurance company which has the option of investing in a risky asset and a risk-free asset, whose price parameters are driven by a finite state Markov chain. The risk process of the insurance company is modeled as a diffusion process whose diffusion and drift parameters switch over time according to the same Markov chain. We study the Markov-modulated mean-variance problem for the insurer and derive explicitly the closed form of the efficient strategy and efficient frontier. In the case of no regime switching, we can see that the efficient frontier in our paper coincides with that of [10] when there is no pure jump.

Portfolio Choice under the Mean-Variance Model with Parameter Uncertainty

Assuming the investor is uncertainty-aversion,the multiprior approach is applied to studying the problem of portfolio choice under the uncertainty about the expected return of risky asset based on the mean-variance model. By introducing a set of constraint constants to measure uncertainty degree of the estimated expected return,it built the max-min model of multi-prior portfolio,and utilized the Lagrange method to obtain the closed-form solution of the model,which was compared with the mean-variance model and the minimum-variance model; then,an empirical study was done based on the monthly returns over the period June 2011 to May 2014 of eight kinds of stocks in Shanghai Exchange 50 Index. Results showed,the weight of multi-prior portfolio was a weighted average of the weight of mean-variance portfolio and that of minimumvariance portfolio; the steady of multi-prior portfolio was strengthened compared with the mean-variance portfolio; the performance of multi-prior portfolio was greater than that of minimum-variance portfolio. The study demonstrates that the investor can improve the steady of multi-prior portfolio as well as its performance for some appropriate constraint constants.

A Mean-variance Problem in the Constant Elasticity of Variance(CEV) Model

In this paper, we focus on a constant elasticity of variance （CEV） modeland want to find its optimal strategies for a mean-variance problem under two constrainedcontrols： reinsurance/new business and investment （no-shorting）. First, aLagrange multiplier is introduced to simplify the mean-variance problem and thecorresponding Hamilton-Jacobi-Bellman （HJB） equation is established. Via a powertransformation technique and variable change method, the optimal strategies withthe Lagrange multiplier are obtained. Final, based on the Lagrange duality theorem,the optimal strategies and optimal value for the original problem （i.e., the efficientstrategies and efficient frontier） are derived explicitly.

Bounds for Goal Achieving Probabilities of Mean-Variance Strategies with a No Bankruptcy Constraint

We establish, through solving semi-infinite programming problems, bounds on the probability of safely reaching a desired level of wealth on a finite horizon, when an investor starts with an optimal mean-variance financial investment strategy under a non-negative wealth restriction.

Goal Achieving Probabilities of Mean-Variance Strategies in a Market with Regime-Switching Volatility

In this paper, we establish properties for the switch-when-safe mean-variance strategies in the context of a Black-Scholes market model with stochastic volatility processes driven by a continuous-time Markov chain with a finite number of states. More precisely, expressions for the goal-achieving probabilities of the terminal wealth are obtained and numerical comparisons of lower bounds for these probabilities are shown for various market parameters. We conclude with asymptotic results when the Markovian changes in the volatility parameters appear with either higher or lower frequencies.

The Impact of General Correlation Under Multi-Period Mean-Variance Asset-Liability Portfolio Management

This paper studies the multi-period mean-variance(MV)asset-liability portfolio management problem(MVAL),in which the portfolio is constructed by risky assets and liability.It is worth mentioning that the impact of general correlation is considered,i.e.,the random returns of risky assets and the liability are not only statistically correlated to each other but also correlated to themselves in different time periods.Such a model with a general correlation structure extends the classical multiperiod MVAL models with assumption of independent returns.The authors derive the explicit portfolio policy and the MV efficient frontier for this problem.Moreover,a numerical example is presented to illustrate the efficiency of the proposed solution scheme.

Continuous-Time Mean-Variance Portfolio Selection Under Non-Markovian Regime-Switching Model with Random Horizon

This paper considers a continuous-time mean-variance portfolio selection with regime-switching and random horizon.Unlike previous works,the dynamic of assets are described by non-Markovian regime-switching models in the sense that all the market parameters are predictable with respect to the filtration generated jointly by Markov chain and Brownian motion.The Markov chain is assumed to be independent of Brownian motion,thus the market is incomplete.The authors formulate this problem as a constrained stochastic linear-quadratic optimal control problem.The authors derive closed-form expressions for both the optimal portfolios and the efficient frontier.All the results are different from those in the problem with fixed time horizon.

Theoretical mean-variance relationship of IP network traffic based on ON/OFF model

Mean-variance relationship （MVR）, nowadays agreed in power law form, is an important function. It is currently used by traffic matrix estimation as a basic statistical assumption. Because all the existing papers obtain MVR only through empirical ways, they cannot provide theoretical support to power law MVR or the definition of its power exponent. Furthermore, because of the lack of theoretical model, all traffic matrix estimation methods based on MVR have not been theoretically supported yet. By observing both our laboratory and campus network for more than one year, we find that such an empirical MVR is not sufficient to describe actual network traffic. In this paper, we derive a theoretical MVR from ON/OFF model. Then we prove that current empirical power law MVR is generally reasonable by the fact that it is an approximate form of theoretical MVR under specific precondition, which can theoretically support those traffic matrix estimation algorithms of using MVR. Through verifying our MVR by actual observation and public DECPKT traces, we verify that our theoretical MVR is valid and more capable of describing actual network traffic than power law MVR.

Optimal Time-consistent Investment and Reinsurance Strategy for Mean-variance Insurers Under the Inside Information

In this paper, we consider the problem of the optimal time-consistent investment and proportional reinsurance strategy under the mean-variance criterion, in which the insurer has some inside information at her disposal concerning the future realizations of her claims process. It is assumed that the surplus of the insurer is governed by a Brownian motion with drift, and the insurer has the possibility to reduce the risk by purchasing proportional reinsurance and investing in financial markets. We first formulate the problem and provide a verification theorem on the extended Hamilton-Jacobi-Bellman equations. Then, the closed-form expression is obtained for the optimal strategy of the optimization problem.

Mean-Field Maximum Principle for Optimal Control of Forward–Backward Stochastic Systems with Jumps and its Application to Mean-Variance Portfolio Problem

We study mean-field type optimal stochastic control problem for systems governed by mean-field controlled forward-backward stochastic differential equations with jump processes,in which the coefficients depend on the marginal law of the state process through its expected value.The control variable is allowed to enter both diffusion and jump coefficients.Moreover,the cost functional is also of mean-field type.Necessary conditions for optimal control for these systems in the form of maximum principle are established by means of convex perturbation techniques.As an application,time-inconsistent mean-variance portfolio selectionmixed with a recursive utility functional optimization problem is discussed to illustrate the theoretical results.

Time-Consistent Portfolio Policy for Asset-Liability Mean-Variance Model with State-Dependent Risk Aversion

In reality,when facing a multi-period asset-liability portfolio selection problem,the risk aversion attitude of a mean-variance investor may depend on the wealth level and liability level.Thus,in this paper,we propose a state-dependent risk aversion model for the investor,in which risk aversion is a linear function of current wealth level and current liability level.Due to the time inconsistency of the resulting multi-period asset-liability mean-variance model,we investigate its time-consistent portfolio policy by solving a nested mean-variance game formulation.We derive the analytical time-consistent portfolio policy,which takes a linear form of current wealth level and current liability level.We also analyze the influence of the risk aversion coefficients on the time-consistent portfolio policy and the investment performance via a numerical example.

Optimal Reinsurance and Investment Strategies Under Mean-Variance Criteria:Partial and Full Information

This paper is concerned with an optimal reinsurance and investment problem for an insurance firm under the criterion of mean-variance. The driving Brownian motion and the rate in return of the risky asset price dynamic equation cannot be directly observed. And the short-selling of stocks is prohibited. The problem is formulated as a stochastic linear-quadratic control problem where the control variables are constrained. Based on the separation principle and stochastic filtering theory, the partial information problem is solved. Efficient strategies and efficient frontier are presented in closed forms via solutions to two extended stochastic Riccati equations. As a comparison, the efficient strategies and efficient frontier are given by the viscosity solution to the HJB equation in the full information case. Some numerical illustrations are also provided.

Mean-variance Hedging for Pricing European-type Contingent Claims with Transaction Costs

In this paper, a European-type contingent claim pricing problem withtransaction costs is considered by a mean-variance hedging argument. The investor has to paytransaction costs which are proportional to the amount of stock transacted. The writer's hedgingobject is to minimize the hedging risk, defined as the variance of hedging error at expiration, witha proper expected excess return level. At first, we consider the mean-variance hedging problem: forinitial hedging wealth f, maximizing the excess expected return under the minimum hedging risklevel V_0. On the other hand, we consider a mean-variance portfolio problem, which is to maximizethe expected return with initial wealth 0 under the same risk level V_0. The minimum initial hedgingwealth f, which can offset the difference of the maximum expected return of these two problems, isthe writer's price.

Discrete Time Mean-variance Analysis with Singular Second Moment Matrixes and an Exogenous Liability

We apply the dynamic programming methods to compute the analytical solution of the dynamic mean-variance optimization problem affected by an exogenous liability in a multi-periods market model with singular second moment matrixes of the return vector of assets. We use orthogonai transformations to overcome the difficulty produced by those singular matrixes, and the analytical form of the efficient frontier is obtained. As an application, the explicit form of the optimal mean-variance hedging strategy is also obtained for our model.

MEAN-VARIANCE MODEL BASED ON FILTERS OF MINIMUM SPANNING TREE

This study aims to reduce the statistical uncertainty of the correlation coefficient matrix in the mean-variance model of Markowitz. A filtering algorithm based on minimum spanning tree （MST） is proposed. Daily data of the 30 stocks of the Hang Seng Index （HSI） and Dow Jones Index （DJI） from 2004 to 2009 are selected as the base dataset. The proposed algorithm is compared with the Markowitz method in terms of risk, reliability, and effective size of the portfolio. Results show that （1） although the predicted risk of portfolio built with the MST is slightly higher than that of Markowitz, the realized risk of MST filtering algorithm is much smaller; and （2） the reliability and the effective size of filtering algorithm based on MST is apparently better than that of the Markowitz portfolio. Therefore, conclusion is that filtering algorithm based on MST improves the mean-variance model of Markowitz.

Portfolio Selection with Random Liability and Affine Interest Rate in the Mean-Variance Framework

This paper studies a dynamic mean-variance portfolio selection problem with random liability in the affine interest rate environment, where the financial market consists of three assets: one risk-free asset, one risky asset and one zero-coupon bond. Assume that short rate is driven by affine interest rate model and liability process is described by the drifted Brownian motion, in addition, stock price dynamics is affected by interest rate dynamics. The investors expect to look for an optimal strategy to minimize the variance of the terminal surplus for a given expected terminal surplus. The efficient strategy and the efficient frontier are explicitly obtained by applying dynamic programming principle and Lagrange duality theorem. A numerical example is given to illustrate our results and some economic implications are analyzed.

Optimal mean-variance reinsurance and investment strategy with constraints in a non-Markovian regime-switching model

This paper is devoted to study the proportional reinsurance/new business and investment problem under the mean-variance criterion in a continuous-time setting.The strategies are constrained in the non-negative cone and all coefficients in the model except the interest rate are stochastic processes adapted the filtration generated by a Markov chain.With the help of a backward stochastic differential equation driven by the Markov chain,we obtain the optimal strategy and optimal cost explicitly under this non-Markovian regime-switching model.The cases with one risky asset and Markov regime-switching model are considered as special cases.

Survey on Multi-period Mean-Variance Portfolio Selection Model

Due to the non-separability of the variance term,the dynamic mean-variance(MV)portfolio optimization problem is inherently difficult to solve by dynamic programming.Li and Ng(Math Finance 10(3):387-406,2000)and Zhou and Li(Appl Math Optim 42(1):19-33,2000)develop the pre-committed optimal policy for such a problem using the embedding method.Following this line of research,researchers have extensively studied the MV portfolio selection model through the inclusion of more practical investment constraints,realistic market assumptions and various financial applications.As the principle of optimality no longer holds,the pre-committed policy suffers from the time-inconsistent issue,i.e.,the optimal policy computed at the intermediate time t is not consistent with the optimal policy calculated at any time before time t.The time inconsistency of the dynamic MV model has become an important yet challenging research topic.This paper mainly focuses on the multi-period mean–variance(MMV)portfolio optimization problem,reviews the essential extensions and highlights the critical development of time-consistent policies.

Time-consistent investment and reinsurance strategies for insurers under multi-period mean-variance formulation with generalized correlated returns

The existing literature on investment and reinsurance is limited to the study of continuous-time problems,while discrete-time problems are always ignored by re-searchers.In this study,we first discuss a multi-period investment and reinsurance opti-mization problem under the classical mean-variance framework.When the asset returns with a serially correlated structure,the time-consistent investment and reinsurance strategies are acquired via backward induction.In addition,we propose an alternative time-consistent mean-variance optimization model that contrasts with the classical mean-variance model,and the corresponding optimal strategy and value function are also derived.We find that the investment and reinsurance strategies are both independent of the current wealth for the above two optimization problems,which coincides with the conclusion presented in the continuous-time problems.Most importantly,the above in-vestment strategies with serially correlated structures are both conditional mean-based strategies,rather than unconditional ones.Finally,we compare the investment and rein-surance strategies suggested above based on the simulation approach,to shed light on which investment-reinsurance strategies are more suitable for insurers.