American Institute of Mathematical Sciences

In business, enterprises need to maintain stable cash flows to meet the demands for payments in order to reduce the probability of possible bankruptcy. In this paper, we propose the optimal cash holding models in terms of continuous time and managers' risk preference in the framework of stochastic control theory in the setting of cash balance accounting with the interval of a safe area for cash holdings. Formulas for the optimal cash holdings are analytically derived with a widely used family of power utility functions. Our models can be seen as an extension of Miller-Orr model to solve the cash holding problem of continuous time from the accounting perspective. Numerical examples are also provided to illustrate the feasibility of the developed optimal cashing holding models of continuous time.

In this paper, the \begin{document}$\mathcal{H}_∞$\end{document} filtering problem of switched nonlinear system with linear hyper plane switching surface is investigated. A state projection method is introduced to ensure the stability of error system and guarantee a prescribed disturbance attenuation level in the \begin{document}$\mathcal{H}_∞$\end{document} sense, by designing filter gains for each subsystem via solving a set of LMIs and formulating a state projection relation for filter state at switching instant. It is worthwhile to note that the state projection relation is deduced by both Lyapunov functions and the switching surface, which implies the state projection method is suitable for switched system with linear hyper plane switching surface. Finally, a numerical example is provided to illustrate our theoretic findings in this paper.

In this paper, we consider a spectrally negative Lévy insurance risk process with a barrier-type dividend strategy. In contrast to the traditional barrier strategy in which dividends are payable to the shareholders immediately when the surplus process reaches a fixed level b (as long as ruin has not yet occurred), it is assumed that the insurer only makes dividend decisions at some discrete time points in the spirit of [1]. Under such a dividend strategy with Erlang inter-dividend-decision times, expressions for the Gerber-Shiu expected discounted penalty function proposed in [24] and the moments of total discounted dividends payable until ruin are derived. The results are expressed in terms of the scale functions of a spectrally negative Lévy process and an embedded spectrally negative Markov additive process. Our analyses rely on the introduction of a potential measure associated with an Erlang random variable. Numerical illustrations are also given.

In this paper, we consider parametric strong vector quasiequilibrium problems in Hausdorff topological vector spaces. Firstly, we introduce parametric gap functions for these problems, and study the continuity property of these functions. Next, we present two key hypotheses related to the gap functions for the considered problems and also study characterizations of these hypotheses. Then, afterwards, we prove that these hypotheses are not only sufficient but also necessary for the Hausdorff lower semicontinuity and Hausdorff continuity of solution mappings to these problems. Finally, as applications, we derive several results on Hausdorff (lower) continuity properties of the solution mappings in the special cases of variational inequalities of the Minty type and the Stampacchia type.

It becomes increasingly important to manage water and improve the efficiency of irrigation under higher temperatures and irregular precipitation patterns. The choice of investment in water saving technologies and its timing play key roles in improving efficiency of water use. In this paper, we use a real option approach to establish a model to handle future uncertainties about the water price. In addition, to match the practical situation, the expiration of the real option is considered to be finite in our model, such that it is difficult to solve the model. Therefore, we reformulate the problem into a linear parabolic variational inequality (Ⅵ) and develop a power penalty method to solve it numerically. Thus, a nonlinear partial differential equation (PDE) is obtained, which is shown to be uniquely solvable and the solution of the nonlinear PDE converges to that of the Ⅵ at the rate of \begin{document}$O(λ^{-\frac{k}{2}})$\end{document} with \begin{document}$λ$\end{document} being the penalty number. Furthermore, a so-called fitted finite volume method is proposed to solve the nonlinear PDE. Finally, several numerical experiments are performed. It is shown that the subjective discount rate will affect the investment boundary mostly, and the flexibility to suspend operation will enlarge the investment region.

This paper investigates a dual-channel supply chain, where one national brand manufacturer has both online and retail channels. The retailer is assumed to sell the national brand as well as his store brand to customers. The following five scenarios are considered: Centralized case, Stackelberg-manufacturer (SM) game, Stackelberg-retailer (SR) game, Nash-manufacturer (NM) game and Nash-retailer (NR) game. The paper derives the conditions under which the supply chain members would like to participate in cooperative advertising. The results show that in the Stackelberg games, the leader in Stackelberg game will reduce its investment in cooperative advertising when it gets a lower marginal profit from the cooperative advertising; In addition, the dual-channel supply chain can get a higher profit if it is dominated by the member whose marginal profit from cooperative advertising is higher. In the Nash games, in order to increase the whole supply chain's profit, the member who has a higher marginal profit in the cooperative advertising should give up the decision power on cost-sharing rate voluntarily. In addition, if there exists a leader in the supply chain, the cooperative advertising will be higher. Furthermore, the introduction of store brand will trigger the manufacturer's antipathy for the low profit.

Based on a monopoly model in industrial symbiosis chain including one upstream manufacturer and one downstream manufacturer, the price sensitive-environmental concern demand is introduced into the paper. The decision behaviors of the manufacturers in industrial symbiosis chain under environmental regulations imposed by the policy makers or the government in waste emission standard, waste emission tax and subsidy for waste usage are investigated. The results show the operational factors of the manufacturers must be taken into account in the right formulation of waste emission standard, and the simultaneous implementation of waste emission tax and subsidy for external environmental performance of the manufacturers is superior to a single policy. Environmental concerned consumers with stronger green attitude who are more willing to buy environmentally friendly products could pressurize the manufacturers into decreasing waste emission level, and the manufacturers will affirmatively involve in industrial symbiosis chain due to the intervention of environmental regulations. Especially, integrated industrial symbiosis becomes the optimal decision for the manufacturers to boost both economic benefit and environmental performance. Waste emission contract and quantity discount contract can be techniques to improve the performance of non-integrated industrial symbiosis chain.

A product service supply chain (PSSC) supplies customers with product-service systems (PSS) consist of integrated products and services. The product manufacturing should match the service supply in the order delivery planning. For PSS orders are usually delivered under time window constraints, this paper is concerned with the integrated order acceptance and scheduling (OAS) decision of the PSSC. Defined the PSS orders by their revenues, product processing times, serving offering times and hard time window constraints, we formulate the OAS problem as a MILP model to optimize total revenue of PSSC and propose two effective value for big-M to solve the problem with small size optimally. The simulated annealing algorithm based on the priority rule of servable orders first (SOF-SA) and the dynamic acceptance and scheduling heuristic (DASH) algorithm are presented. The performance of the model and the two algorithms are proved through simulating instances with different order sizes. Computational tests show that the SOF-SA algorithm is more effective when used for small size problems while the DASH algorithm is more effective for problems with larger size; negotiating with customers to make reasonable delivery time windows should be beneficial to increasing total revenue and improving the decision efficiency.

In this paper, we consider a class of optimal switching control problems with multiple time-delays and a cost on changing control and subject to terminal state constraints. A computational method involving three stages is developed to solve this class of optimal control problems. First, by parameterizing the control function with piecewise-constant functions, the optimal switching control problem is approximated by a sequence of finite-dimensional optimization problems, where the original switching times, the control heights and the control switching times are decision variables. Second, by introducing new variables, the total variation of the control variables is transformed into an equivalently smooth function. Third, we convert the constrained optimization problem into one only with box constraints by an exact penalty function method. The gradients of the cost functional are then derived, which can be combined with any gradient-based optimization method to determine the optimal solution. Finally, a numerical example is given to illustrate the effectiveness of the proposed algorithm.

In this paper, we consider a Wishart Affine Stochastic Correlation (WASC) model which accounts for the stochastic volatilities of the assets and for the stochastic correlations not only between the underlying assets' returns but also between their volatilities. Under the assumptions of the model, we derive the neutral and indifference pricing for general European-style financial contracts. The paper shows that comparing to risk-neutral pricing, the utility-based pricing methods are generally feasible and avoid factitiously dealing with some risk premia corresponding to the volatilities-correlations as a consequence of the incompleteness of the market.

Consider a bivariate Lévy-driven risk model in which the loss process of an insurance company and the investment return process are two independent Lévy processes. Under the assumptions that the loss process has a Lévy measure of consistent variation and the return process fulfills a certain condition, we investigate the asymptotic behavior of the finite-time ruin probability. Further, we derive two asymptotic formulas for the finite-time and infinite-time ruin probabilities in a single Lévy-driven risk model, in which the loss process is still a Lévy process, whereas the investment return process reduces to a deterministic linear function. In such a special model, we relax the loss process with jumps whose common distribution is long tailed and of dominated variation.

This paper is concerned with studying an optimal multi-period asset-liability mean-variance portfolio selection with probability constraints using mean-field formulation without embedding technique. We strictly derive its analytical optimal strategy and efficient frontier. Numerical examples shed light on efficiency and accuracy of our method when dealing with this class of multi-period non-separable mean-variance portfolio selection problems.

This paper considers an imperfect production system to obtain the optimal production run time and inspection policy. Contrary to the existing literature this model considerers that product inspection performs at any arbitrary time of the production cycle and after the inspection, all defective products produced until the end of the production run are fully reworked. Due to some misclassification during inspection, from the inspector's side two types of inspection errors as Type Ⅰ and Type Ⅱ are considered to make the model more realistic rather than existing models. Defective items, found by the inspector, are salvaged at some cost before being shipped. Non-inspected defective items are passed to customers with free minimal repair warranty. The model gives three special cases, where it is found that this model converges over the exiting literature. Some numerical examples along with graphical representations are provided to illustrate the proposed model with comparison with the existing models. Sensitivity analysis of the optimal solution with respect to key parameters of the model has been carried out and the implications are discussed.

The objective of this manuscript is to present some new interactive geometric aggregation operators for the interval-valued intuitionistic fuzzy numbers (IVIFNs). In order to achieve it, firstly the shortcomings of the existing operators have been highlighted and then resolved it by defining new operational laws based on the pairs of hesitation degree between the membership functions. By using these improved laws, some geometric aggregation operators, namely interval-valued intuitionistic fuzzy Hamacher interactive weighted and hybrid geometric labeled as IIFHIWG and IIFHIHWG operators, respectively have been proposed. Furthermore, desirable properties corresponding to these operators have been stated. Finally, a decision-making method based on the proposed operator has been illustrated to demonstrate the approach. A computed result is compared with the existing results.

Portfolio selection is widely recognized as the birth-place of modern finance; portfolio optimization has become a developed tool for portfolio selection by the endeavor of generations of scholars. Multiple optima are an important aspect of optimization. Unfortunately, there is little research for multiple optima of portfolio optimization. We present examples for the multiple optima, emphasize the risk of overlooking the multiple optima by (ordinary) quadratic programming, and report the software failure by parametric quadratic programming. Moreover, we study multiple optima of multiple-objective portfolio selection and prove the nonexistence of the multiple optima of an extension of the model of Merton. This paper can be a step-stone of studying the multiple optima.

This paper studies the evolutionary stable strategies and preferences regarding corporate social responsibility of competing firms. Firms randomly compete with each other in pairs. Shareholder-oriented firms have no social responsibility concern, whereas a firm that is concerned with social responsibility is stakeholder-oriented. Each firm first picks one of two production strategies: shareholder-oriented or stakeholder-oriented, and then decides production quantity. We find that socially responsible firms have lower retail prices. The evolutionary stability of a strategy depends on product substitutability and the degree to which firms care about social responsibility. When product substitutability is relatively high, stakeholder-oriented strategy is the evolutionary stable strategy; if product substitutability is lower than a threshold, shareholder-oriented strategy is evolutionary stable; and with moderate product substitutability, both strategies are evolutionary stable.

Furthermore, we consider how the degree of social responsibility preference evolves according to the adaptive dynamics to continuously stable preference. We find that the non social responsibility concern behavior is not an evolutionary stable preference; there is a unique continuously stable degree of social responsibility preference. Furthermore, we find the evolutionary stability of shareholder-oriented and stakeholder-oriented depends on the initial distribution of firms' strategies under the continuously stable social responsibility preference.

Gift cards is frequently used to replace traditional gift cash and gift products, especially when gift givers do not know gift receivers' performances. Basing on this phenomenon, we analyze the supplier's and the retailer's strategies with selling gift cards. First, we develop a Stackelberg model without selling gift cards. Next, we develop two models with selling gift cards when unredeemed gift cards balances become the retailer's property and the state's property, respectively. We present the optimal solutions and exam the impacts of parameters on the optimal decisions and the supply chain performance. When the retailer sells gift cards, the optimal order quantity is smaller than that without selling gift cards. The optimal wholesale price with selling gift cards is related to the treatment of unredeemed gift card balances. When unredeemed gift cards balances become the retailer's property, the wholesale price is lower than that without selling gift cards. However, when unredeemed gift cards balances become the state's property, the wholesale price is lower than that without selling gift cards in some conditions. And with selling gift cards, the optimal expected profits of retailer and supply chain are better off, but the optimal expected profit of supplier is worse off.

This article deals with an optimal dividend, reinsurance and capital injection control problem in the diffusion risk model. Under the objective of maximizing the insurance company's value, we aim at finding the joint optimal control strategy. We assume that there exist both the fixed and proportional costs in control processes and the excess-of-loss reinsurance is "expensive". We derive the closed-form solutions of the value function and optimal strategy by using stochastic control methods. Some economic interpretations of the obtained results are also given.

We propose a modified splitting method for a linearly constrained minimization model whose objective function is the sum of three convex functions without coupled variables. Our work is mainly inspired by the recently proposed strictly contractive Peaceman-Rachford splitting method (SC-PRSM) for a two-block separable convex minimization model. For the new method, we prove its convergence and estimate its convergence rates measured by iteration complexity in the nonergodic sense. We also test the SC-PRSM on the continuous resource allocation problem, and the numerical results show that our method has a competitive performance with the direct extension of ADMM which usually works well in practice but may fail to converge in theory.

The problem of solving periodic Sylvester matrix equations is discussed in this paper. A new kind of iterative algorithm is proposed for constructing the least square solution for the equations. The basic idea is to develop the solution matrices in the least square sense. Two numerical examples are presented to illustrate the convergence and performance of the iterative method.