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In most exiting portfolio selection models, security returns are assumed to have random or fuzzy distributions. However, uncertainties exist in actual financial markets. Markets are associated not only with inherent risk, but also with background risk that results from the differences among individual investors. This paper investigated the compliance of stock yields to the fuzzy-natured high-order moments of random numbers in order to develop a high-moment trapezoidal fuzzy random portfolio risk model based on variance, skewness, and kurtosis. Data obtained from the Shanghai Stock Exchange and Shenzhen Stock Exchange was used to assess the influence on the proposed model of both background risk and the maximum level of satisfaction of the portfolio. The empirical results demonstrated that the differences between the maximum and minimum variance, skewness, and kurtosis values of the portfolio were positively correlated with the variance of the background risk.

In this paper we reanalyze Said’s (2011) work by retaining all his assumptions except that we use the first-price auction to sell differentiated goods to buyers in dynamic markets instead of the second-price auction. We conclude that except for the expression of the equilibrium bidding strategy, all the results for the first-price auction are exactly the same as the corresponding ones for the second-price auction established by Said (2011). This implies that the well-known “revenue equivalence theorem” holds true for Said’s (2011) dynamic model setting.

This paper considers a worst-case investment optimization problem with delay for a fund manager who is in a crash-threatened financial market. Driven by existing of capital inflow/outflow related to history performance, we investigate the optimal investment strategies under the worst-case scenario and the stochastic control framework with delay. The financial market is assumed to be either in a normal state (crash-free) or in a crash state. In the normal state the prices of risky assets behave as geometric Brownian motion, and in the crash state the prices of risky assets suddenly drop by a certain relative amount, which induces to a dropping of the total wealth relative to that of crash-free state. We obtain the ordinary differential equations satisfied by the optimal investment strategies and the optimal value functions under the power and exponential utilities, respectively. Finally, a numerical simulation is provided to illustrate the sensitivity of the optimal strategies with respective to the model parameters.

The E-supply chain is formed gradually along with the development of network, which is getting more attention among enterprises with unique advantages. Three E-supply chain operation modes are constructed in this paper, then the optimal pricing and advertising strategies under those modes are studied and compared, which are demonstrated with numerical examples. The results of comparison and analysis show that: Selling price, network platform service level, advertising investment and the profits of manufacturer, network platform and E-supply chain all increase with advertising effectiveness of stimulating demand growth. Under centralized decision-making mode, service level is highest, advertising investment is largest and the profit of E-supply chain is highest as well. When manufacturer leads decentralized decision-making mode, not only network service level, advertising investment and the profit of manufacturer can gain better results, but also profit of network platform can be higher while the advertisement effect of increasing demand is big enough. Additionally, it is confirmed that centralized decision-making is better than decentralized decision-making for system operation. Besides, decentralized decision-making mode led by manufacturer is superior to it led by network platform on the condition that advertisement effect is obvious.

We consider an M/M/ 2 queueing system with two-heterogeneous servers and multiple vacations. Customers arrive according to a Poisson process. However, customers become impatient when the system is on vacation. We obtain explicit expressions for the time dependent probabilities, mean and variance of the system size at time t by employing probability generating functions, continued fractions and properties of the modified Bessel functions. Finally, two special cases are provided.

An insurance-package is a combination being tie-in at least two different categories of insurances with different underwriting-yield-rate. In this paper, the optimal insurance-package and investment problem is investigated by maximizing the insurer’s exponential utility of terminal wealth to find the optimal combination-share and investment strategy. Using the methods of stochastic analysis and stochastic optimal control, the Hamilton-Jacobi-Bellman (HJB) equations are established, the optimal strategy and the value function are obtained in closed form. By comparing with classical results, it shows that the insurance-package can enhance the utility of terminal wealth, meanwhile, reduce the insurer’s claim risk.