不完备证券市场中博弈未定权益的保值

考虑不完备证券市场中博弈未定权益(GCC)的保值问题,通过Kramkov关于上鞅的可选分解定理给出未定权益的上保值价格和下保值价格。指出关于买卖双方都存在着一个最优保值策略。给出价格的一个无套利区间,并针对前面的结论,给出几个性质以及在限制投资组合方面的一个应用。     

Cooperative games of choosing partners and forming coalitions in the marketplace

Two games of interacting between a coalition of players in a marketplace and the residual players acting there are discussed, along with two approaches to fair imputation of gains of coalitions in cooperative games that are based on the concepts of the Shapley vector and core of a cooperative game. In the first game, which is an antagonistic one, the residual players try to minimize the coalition's gain, whereas in the second game, which is a noncooperative one, they try to maximize their own gain as a coalition. A meaningful interpretation of possible relations between gains and Nash equilibrium strategies in both games considered as those played between a coalition of firms and its surrounding in a particular marketplace in the framework of two classes of n-person games is presented. A particular class of games of choosing partners and forming coalitions in which models of firms operating in the marketplace are those with linear constraints and utility functions being sums of linear and bilinear functions of two corresponding vector arguments is analyzed, and a set of maximin problems on polyhedral sets of connected strategies which the problem of choosing a coalition for a particular firm is reducible to are formulated based on the firm models of the considered kind.     

拟鞅分解及非完备市场未定权益的保值

证明了拟鞅可选分解定理,并应用这种分解解决非完备金融市场欧式及美式未定权益的保值问题。     

Majority voting leads to unanimity

We consider a situation where society decides, through majority voting in a secret ballot, between the alternatives of ‘reform’ and ‘status quo’. Reform is assumed to create a minority of winners, while being efficient in the Kaldor–Hicks sense. We explore the consequences of allowing binding transfers between voters conditional on the chosen alternative. In particular, we establish conditions under which the winners wish to compensate all losers, thus leading to unanimity for reform, rather than compensating some losers to form a non-maximal majority. The analysis employs concepts from cooperative game theory.      

The fuzzy core in games with fuzzy coalitions

In this paper, the fuzzy core of games with fuzzy coalition is proposed, which can be regarded as the generalization of crisp core. The fuzzy core is based on the assumption that the total worth of a fuzzy coalition will be allocated to the players whose participation rate is larger than zero. The nonempty condition of the fuzzy core is given based on the fuzzy convexity. Three kinds of special fuzzy cores in games with fuzzy coalition are studied, and the explicit fuzzy core represented by the crisp core is also given. Because the fuzzy Shapley value had been proposed as a kind of solution for the fuzzy games, the relationship between fuzzy core and the fuzzy Shapley function is also shown. Surprisingly, the relationship between fuzzy core and the fuzzy Shapley value does coincide, as in the classical case.     

Cooperative facility location games

The location of facilities in order to provide service for customers is a well-studied problem in the operations research literature. In the basic model, there is a predefined cost for opening a facility and also for connecting a customer to a facility, the goal being to minimize the total cost. Often, both in the case of public facilities (such as libraries, municipal swimming pools, fire stations, … ) and private facilities (such as distribution centers, switching stations, … ), we may want to find a ‘fair’ allocation of the total cost to the customers—this is known as the cost allocation problem. A central question in cooperative game theory is whether the total cost can be allocated to the customers such that no coalition of customers has any incentive to build their own facility or to ask a competitor to service them. We establish strong connections between fair cost allocations and linear programming relaxations for several variants of the facility location problem. In particular, we show that a fair cost allocation exists if and only if there is no integrality gap for a corresponding linear programming relaxation; this was only known for the simplest unconstrained variant of the facility location problem. Moreover, we introduce a subtle variant of randomized rounding and derive new proofs for the existence of fair cost allocations for several classes of instances. We also show that it is in general NP-complete to decide whether a fair cost allocation exists and whether a given allocation is fair.     

A note on maximal covering location games

In this note we introduce and analyze maximal covering location games. As the core may be empty, several sufficient conditions for core non-emptiness are presented. For each condition we provide an example showing that when the condition is not satisfied, core non-emptiness is not guaranteed.     

A general framework for cooperation under uncertainty

In this paper, we introduce a general framework for situations with decision making under uncertainty and cooperation possibilities. This framework is based upon a two stage stochastic programming approach. We show that under relatively mild assumptions the associated cooperative games are totally balanced. Finally, we consider several example situations.     

残缺区间合作博弈及其在农地污染治理中的应用

针对联盟收益值部分未知的区间合作博弈,定义了残缺区间合作博弈的相关概念。基于合作博弈的超可加性,建立了联盟区间收益值的一致性验证模型。通过构造正、负理想分配及其与收益分配向量之间的偏差,给出了残缺区间合作博弈的区间Ideal-Shapley值求解模型,分析了区间Ideal-Shapley值的合理性与存在性。利用上述模型求解农地污染联合治理的节约成本分摊策略,验证了区间Ideal-Shapley值求解模型的有效性。     

The nucleon of cooperative games and an algorithm for matching games

Thenucleon is introduced as a new allocation concept for non-negative cooperativen-person transferable utility games. The nucleon may be viewed as the multiplicative analogue of Schmeidler’s nucleolus. It is shown that the nucleon of (not necessarily bipartite) matching games can be computed in polynomial time.     

On the cooperation of recycling operations

This paper addresses two important issues that may affect the operations efficiency in the recycling industry. First, the industry contains many small-scale and inefficient recycling firms, especially in developing countries. Second, the output from recycling a waste product often yields multiple recycled products that cannot all be sold efficiently by a single firm. To address these two issues, this paper examines how different firms can cooperate in their recycling and pricing decisions using cooperative game theory. Recycling operations under both joint and individual productions with different cost structures are considered. Decisions include the quantity of waste product to recycle and the price at which to sell each recycled product on each firm’s market. These decisions can be made jointly by multiple cooperating firms to maximize total profit. We design allocation schemes for maximized total profit to encourage cooperation among all firms. Managerial insights are provided from both environmental and economic perspectives.     

Resource location games

In this paper, we introduce and analyze resource location games. We show core non-emptiness by providing a set of intuitive core allocations, called Resource-Profit allocations. In addition, we present a sufficient condition for which the core and the set of Resource-Profit allocations coincide. Finally, we provide an example showing that when the sufficient condition is not satisfied, the coincidence is not guaranteed.     

Assignment markets that are uniquely determined by their core

A matrix A defines an assignment market, where each row represents a buyer and each column a seller. If buyer i is matched with seller j, the market produces a_ij units of utility. Quint (1991) points out that usually many different assignment matrices exist that define markets with the same core and poses the question of when the matrix is uniquely determined by the core of the related market. We characterize these matrices in terms of a strong form of the doubly dominant diagonal property. A matching between buyers and sellers is optimal if it produces the maximum units of utility. Our characterization allows us to show that the number of optimal matchings in markets uniquely characterized by their core is a power of two.     

On characterization of the core of lane covering games via dual solutions

The lane covering game (LCG) is a cooperative game where players cooperate to reduce the cost of cycles that cover their required lanes on a network. We discuss the possibilities/impossibilities of a complete characterization of the core via dual solutions in LCGs played among a collection of shippers, each with a number of service requirements along some lanes, and show that such a complete characterization is possible if each shipper has at most one service requirement.     

Differentiability in optimization theory 1

This paper deals with necessary conditions for optimization problems with infinitely many inequality constraints assuming various differentiability conditions. By introducing a second topology N on a topological vector space we define generalized versions of differentiability and tangential cones. Different choices of N lead to Gâteaux-, Hadamaed- and weak differentiability with corresponding tangential cones. The general concept is used to derive necessary conditions for local optimal points in form of inequalities and generalized multiplier rules, Special versions of these theorems are obtained for different differentiability assumptions by choosing properly. An application to approximation theory is given.     

Stock Loans in Incomplete Markets

Abstract

A stock loan is a contract whereby a stockholder uses shares as collateral to borrow money from a bank or financial institution. In Xia and Zhou (2007 Xia, J. and Zhou, X. Y. 2007. Stock loans. Mathematical Finance, 17(2): 307–317. [Crossref], [Web of Science ®] , [Google Scholar], Stock loans, Mathematical Finance, 17(2), pp. 307–317), this contract is modelled as a perpetual American option with a time-varying strike and analysed in detail within a risk-neutral framework. In this paper, we extend the valuation of such loans to an incomplete market setting, which takes into account the natural trading restrictions faced by the client. When the maturity of the loan is infinite, we use a time-homogeneous utility maximization problem to obtain an exact formula for the value of the loan fee to be charged by the bank. For loans of finite maturity, we characterize the fee using variational inequality techniques. In both cases, we show analytically how the fee varies with the model parameters and illustrate the results numerically.     

Cooperation under interval uncertainty

In this paper, the classical theory of two-person cooperative games is extended to two-person cooperative games with interval uncertainty. The core, balancedness, superadditivity and related topics are studied. Solutions called ψ ^α-values are introduced and characterizations are given.