与两种破产类型相关的余额极值联合分布

带干扰古典风险模型具有由索赔和小余额快速变化分别引起的两种破产和相应的破产时间．该文在两种类型破产各自发生的条件下,使用破产概率函数分别就余额过程首次返回零点以及最后一次返回零点所经历的时间间隔,给出了各自的余额最大值和最小值的联合分布．文章还给出了与该风险模型关联密切的若干鞅的表达式．     

On the saddle-point stability for a class of dynamic games

In this paper, we study the stability properties of the class of capital accumulation games introduced by Fershtman and Muller (Ref. 1). Both discrete and continuous time versions are discussed. It is shown that the open-loop Nash equilibrium solutions for both games are characterized by a general saddle-point property, a result best known from the turnpike literature in optimal growth theory. In the case of zero discount rates, an even stronger result can be derived: As long as the Hessian matrix of the instantaneous profit functions has a quasidominant diagonal, no pure imaginary roots are possible.The authors thank J. Boyd III, G. Feichtinger, S. Jørgensen, and G. Schwann for helpful comments. The first author acknowledges financial support from the Natural Science and Engineering Research Council of Canada, Grant No. OGP-0037342.     

The gold-mine game

The paper considers the following two-person zero-sum game. The minimizing player chooses to hide his gold and a mine in two distinct boxes from an infinite number of boxes labelled 1, 2, 3,.... The maximizing player now chooses to open the boxes in some order, and if he finds the gold before the mine the payoff to him is 1; otherwise, the payoff is zero. The game is solved in the sense of Kindler.     

On Nikaido-Isoda type theorems for discounted stochastic games

We present a class of countable state space stochastic games with discontinuous payoff functions satisfying some assumptions similar to the ones of Nikaido and Isoda for one-stage games. We prove that these games possess stationary equilibria. We show that after adding some concavity assumptions these equilibria are nonrandomized. Further, we present an example of input (or production) dynamic game satisfying the assumptions of our model. We give a closed-form solution for this game.     

Existence of minmax points in discontinuous strategic games

In this note we prove the existence of minmax points for strategic form games where the sets of strategies are topological spaces and the payoff functions satisfy conditions weaker than continuity. The employed tools are the class of transfer weakly upper continuous functions and the class of weakly lower pseudocontinuous functions. An example shows that our result is of minimal character.     

Avoiding unfairness of Owen allocations in linear production processes

This paper deals with cooperation situations in linear production problems in which a set of goods are to be produced from a set of resources so that a certain benefit function is maximized, assuming that resources not used in the production plan have no value by themselves. The Owen set is a well-known solution rule for the class of linear production processes. Despite their stability properties, Owen allocations might give null payoff to players that are necessary for optimal production plans. This paper shows that, in general, the aforementioned drawback cannot be avoided allowing only allocations within the core of the cooperative game associated to the original linear production process, and therefore a new solution set named EOwen is introduced. For any player whose resources are needed in at least one optimal production plan, the EOwen set contains at least one allocation that assigns a strictly positive payoff to such player.     

On the probability of existence of pure equilibria in matrix games

We examine the probability that a randomly chosen matrix game admits pure equilibria and its behavior as the number of actions of the players or the number of players increases. We show that, for zero-sum games, the probability of having pure equilibria goes to zero as the number of actions goes to infinity, but it goes to a nonzero constant for a two-player game. For many-player games, if the number of players goes to infinity, the probability of existence of pure equilibria goes to zero even if the number of actions does not go to infinity.This research was supported in part by NSF Grant CCR-92-22734.     

On the uniqueness of Nash strategies for a class of analytic differential games

The uniqueness of Nash equilibria is shown for the case where the data of the problem are analytic functions and the admissible strategy spaces are restricted to analytic functions of the current state and time.This work was supported in part by the Joint Services Electronics Program (US Army, US Navy, and US Air Force) under Contract No. DAAB-07-72-C-0259, in part by the National Science Foundation under Grant No. ENG-74-20091, and in part by the Department of Energy, Electric Energy Systems Division under Contract No. US ERDA EX-76-C-01-2088.     

服务贸易出口退税政策优化及国际竞争力评价

服务贸易出口退税政策事关服务贸易逆差的缩小及国际竞争力的提升。为探索我国服务贸易出口退税政策的优化方式及其对服务贸易国际竞争力的影响程度,文章构建中国服务贸易出口退税动态可计算一般均衡模型(ET-DCGE),对建筑服务业、旅游业、金融业、咨询业和其他服务业设计包括零税率、免税向零税率过渡和增加退税率档次等方式的出口退税政策优化模拟方案。结果显示,在全部实行零税率政策下,服务业贸易逆差降低程度和国际竞争力提升程度最大。     

The joint distributions of several important actuarial diagnostics in the classical risk model

In this paper we examine the joint distributions of several actuarial diagnostics which are important to insurers’ running in the classical risk model. They include the time of the surplus process leaving zero ultimately (simply, the ultimately leaving-time), the number of zero, the surplus immediately prior to ruin, the deficit at ruin, the supreme and minimum profits before ruin, the supreme profits and deficit until it leaves zero ultimately and so on. We obtain explicit expressions for their joint distributions mainly by strong Markov property of the surplus process—a technique used by Wu et al. (2002) [J. Appl. Math., in press], which is completely different from former contributions on this topic. Further, we give the exact calculating results for them when the individual claim amounts are exponentially distributed.     

Mixed strategy solutions for quadratic games

Mixed strategy solutions are given for two-person, zero-sum games with payoff functions consisting of quadratic, bilinear, and linear terms, and strategy spaces consisting of closed balls in a Hilbert space. The results are applied to linear-quadratic differential games with no information, and with quadratic integral constraints on the control functions.     

A single-item economic lot-sizing problem with a non-uniform resource: Approximation

We study a generalization of the classical single-item capacitated economic lot-sizing problem to the case of a non-uniform resource usage for production. The general problem and several special cases are shown to be non-approximable with any polynomially computable relative error in polynomial time. An optimal dynamic programming algorithm and its approximate modification are presented for the general problem. Fully polynomial time approximation schemes are developed for two NP-hard special cases: (1) cost functions of total production are separable and holding and backlogging cost functions are linear with polynomially related slopes, and (2) all holding costs are equal to zero.     

Quitting games – An example

Quitting games are multi-player sequential games in which, at every stage, each player has the choice between continuing and quitting. The game ends as soon as at least one player chooses to quit; each player i then receives a payoff r _S ⁱ, which depends on the set S of players that did choose to quit. If the game never ends, the payoff to each player is zero.? We exhibit a four-player quitting game, where the “simplest” equilibrium is periodic with period two. We argue that this implies that all known methods to prove existence of an equilibrium payoff in multi-player stochastic games are therefore bound to fail in general, and provide some geometric intuition for this phenomenon. Received: October 2001     

具有两种副索赔的离散相依风险模型破产问题

考虑了一类离散相依的风险模型,该模型假设主索赔以一定的概率引起两种副索赔,而第一种副索赔有可能延迟发生.通过引入一个辅助模型,分别得出了该风险模型初始盈余为0时破产前盈余与破产时赤字的联合分布的表达式、初始盈余为"时破产前盈余和破产时赤字的联合分布的递推公式、初始盈余为0时的破产概率,以及初始盈余为"时的破产概率求解方...     

Equivalence classes of problem instances for a continuous-time lot sizing and scheduling problem

In the context of a single machine, multi-item, continuous-time lot sizing and scheduling problem with a production rate alternating between the two values zero and full production rate, this paper identifies classes of equivalent problem instances which differ from one another in the way in which demand is represented. Each class contains an instance with a continuous cumulated demand function, and may contain demand functions with very different shapes, including functions with discontinuities. When approaching the problem (in order to solve it numerically, or to prove analytical results etc.), it therefore becomes possible to select, from many different representations, the problem instance which best meets the requirements of the applied method.     

Dynamic economic lot size model with perishable inventory and capacity constraints

In this study, we consider a dynamic economic lot sizing problem for a single perishable item under production capacities. We aim to identify the production, inventory and backlogging decisions over the planning horizon, where (i) the parameters of the problem are deterministic but changing over time, and (ii) producer has a constant production capacity that limits the production amount at each period and is allowed to backorder the unmet demand later on. All cost functions are assumed to be concave. A similar problem without production capacities was studied in the literature and a polynomial time algorithm was suggested (Hsu, 2003 [1]). We assume age-dependent holding cost functions and the deterioration rates, which are more realistic for perishable items. Backordering cost functions are period-pair dependent. We prove the NP-hardness of the problem even with zero inventory holding and backlogging costs under our assumptions. We show the structural properties of the optimal solution and suggest a heuristic that finds a good production and distribution plan when the production periods are given. We discuss the performance of the heuristic. We also give a Dynamic Programing-based heuristic for the solution of the overall problem.     

Bicriterion differential games with qualitative outcomes

Combat games are studied as bicriterion differential games with qualitative outcomes determined by threshold values on the criterion functions. Survival and capture strategies of the players are defined using the notion of security levels. Closest approach survival strategies (CASS) and minimum risk capture strategies (MRCS) are important strategies for the players identified as solutions to four optimization problems involving security levels. These are used, in combination with the preference orderings of the qualitative outcomes by the players, to delineate the win regions and the secured draw and mutual kill regions for the players. It is shown that the secured draw regions and the secured mutual kill regions for the two players are not necessarily the same. Simple illustrative examples are given.This paper is based partially on research supported by the Council of Scientific and Industrial Research, India, through a Research Associateship Grant to the second author.     

A stability concept for matrix game optimal strategies and its application to linear programming sensitivity analysis

This paper studies a class of perturbations of a game matrix that alters each row by a different amount. We find that completely mixed optimal strategies are stable under these perturbations provided the norm of the vector of additive amounts is sufficiently small. Using this concept we give a new characterization of completely mixed grames. We also obtain a sensitivity result for a class of perturbations of the technological coefficient matrix of positive linear programs. The stability of an optimal strategy holds throughout at least a spherical neighborhood of the zero perturbation. We give a computational formula and equivalent programming formulations for the radius of this neighborhood.     

Reductions of interval noncooperative games

Noncooperative games of a finite number of persons with interval-valued payoff functions are considered. The concept of an equilibrium situation is introduced. A reduction of such games to deterministic noncooperative games is proposed. Properties of the reduced games are discussed. Interval antagonistic and bimatrix games are examined, and illustrative examples are considered.