Relative Entropy in Determining Degressive Proportional Allocations

The principle of degressively proportional apportionment of goods, being a compromise between equality and proportionality, facilitates the application of many different allocation rules. Agents with smaller entitlements are more interested in an allocation that is as close to equality as possible, while those with greater entitlements prefer an allocation as close to proportionality as possible. Using relative entropy to quantify the inequity of allocation, this paper indicates an allocation that neutralizes these two contradictory approaches by symmetrizing the inequities perceived by the smallest and largest agents participating in the apportionment. First, based on some selected properties, the set of potential allocation rules was reduced to those generated by power functions. Then, the existence of the power function whose exponent is determined so as to generate the allocation that symmetrizes the relative entropy with respect to equal and proportional allocations was shown. As a result, all agents of the apportionment are more inclined to accept the proposed allocation regardless of the size of their entitlements. The exponent found in this way shows the significant relationship between the problem under study and the well-known Theil indices of inequality. The problem may also be seen from this viewpoint.     

分数跳-扩散环境下欧式期权定价的Ornstein-Uhlenbeck模型

假设股票价格遵循分数布朗运动和复合泊松过程驱动的随机微分方程,建立分数跳-扩散Ornstein-Uhlenbeck模型,利用价格过程的实际概率测度和公平保费原理,得到欧式看涨期权定价的解析表达式。推广了关于欧式期权定价的结论。     

Late marriage and transition from arranged marriages to love matches: A search-theoretic approach

ABSTRACT

The aim of this study is to explore the mechanism behind how the spread of individualism, the prevalence of love matches, and the increase in search costs affect late marriages in Japan. To this end, I construct a search-theoretic model, which is a combination of the Markov decision process and the evolution of preferences. I present three results. 1) The spread of individualism is driven by those who moderately consider the social status of their family. 2) The spread of individualism and the prevalence of love matches delay the average marriage timing, but its effect is limited. 3) The diversity of individualism prevents people from switching from love matches to arranged marriages, while the search costs are rising.     

风险投资合约中最优努力与收益分享比的关系

构建了多阶段风险投资的委托代理模型,同时考虑了投资家和企业家两方面的努力,对企业家和投资家的最优努力水平与收益分享系数的关系进行了理论分析和数值模拟,随后考虑了企业家公平偏好对努力水平的影响.发现随着互补程度的增大,两者努力水平对分享系数的反应曲线趋于重合.公平偏好的加入使得投资家和企业家对自身收益更加敏感.     

A Reduced-Load Equivalence for Generalised Processor Sharing Networks with Long-Tailed Input Flows

We consider networks where traffic is served according to the Generalised Processor Sharing (GPS) principle. GPS-based scheduling algorithms are considered important for providing differentiated quality of service in integrated-services networks. We are interested in the workload of a particular flow i at the bottleneck node on its path. Flow i is assumed to have long-tailed traffic characteristics. We distinguish between two traffic scenarios, (i) flow i generates instantaneous traffic bursts and (ii) flow i generates traffic according to an on/off process. In addition, we consider two configurations of feed-forward networks. First we focus on the situation where other flows join the path of flow i. Then we extend the model by adding flows which can branch off at any node, with cross traffic as a special case. We prove that under certain conditions the tail behaviour of the workload distribution of flow i is equivalent to that in a two-node tandem network where flow i is served in isolation at constant rates. These rates only depend on the traffic characteristics of the other flows through their average rates. This means that the results do not rely on any specific assumptions regarding the traffic processes of the other flows. In particular, flow i is not affected by excessive activity of flows with heavier-tailed traffic characteristics. This confirms that GPS has the potential to protect individual flows against extreme behaviour of other flows, while obtaining substantial multiplexing gains.     

On some ordinal models for decision making under uncertainty

In the field of Artificial Intelligence many models for decision making under uncertainty have been proposed that deviate from the traditional models used in Decision Theory, i.e. the Subjective Expected Utility (SEU) model and its many variants. These models aim at obtaining simple decision rules that can be implemented by efficient algorithms while based on inputs that are less rich than what is required in traditional models. One of these models, called the likely dominance (LD) model, consists in declaring that an act is preferred to another as soon as the set of states on which the first act gives a better outcome than the second act is judged more likely than the set of states on which the second act is preferable. The LD model is at much variance with the SEU model. Indeed, it has a definite ordinal flavor and it may lead to preference relations between acts that are not transitive. This paper proposes a general model for decision making under uncertainty tolerating intransitive and/or incomplete preferences that will contain both the SEU and the LD models as particular cases. Within the framework of this general model, we propose a characterization of the preference relations that can be obtained with the LD model. This characterization shows that the main distinctive feature of such relations lies in the very poor relation comparing preference differences that they induce on the set of outcomes. We wish to thank two anonymous referees for their helpful comments on an earlier draft of this text. The usual caveat applies.     

Duality theory for preferences in multiobjective decisionmaking

A duality theory for convex multiobjective decisionmaking is developed. This duality theory is designed for a decisionmaker determining preferred solutions, while duality theories presented earlier have focused on how to generate the whole Pareto optimal set.     

NP-hardness results for the aggregation of linear orders into median orders

Given a collection Π of individual preferences defined on a same finite set of candidates, we consider the problem of aggregating them into a collective preference minimizing the number of disagreements with respect to Π and verifying some structural properties. We study the complexity of this problem when the individual preferences belong to any set containing linear orders and when the collective preference must verify different properties, for instance transitivity. We show that the considered aggregation problems are NP-hard for different types of collective preferences (including linear orders, acyclic relations, complete preorders, interval orders, semiorders, quasi-orders or weak orders), if the number of individual preferences is sufficiently large.     

A comparison of the coordination preferences of Zn, Co, and Cd(II) with the heteroscorpionate ligand (2-hydroxy-3-t-butyl-methylphenyl)bis (3,5-dimethylpyrazolyl)methane

Reaction of the Zn, Cd, or Co nitrate salts with the deprotonated ligand (2-hydroxy-3-t-butyl-methylphenyl)bis(3,5-dimethylpyrazolyl)methane (L1O^–) in methanol produced the following complexes: [(L1OH)Zn(NO₃)₂] in two isomorphs, a = 40.983(8) Å, b = 9.571(2) Å, c = 15.667(8) Å, = 90, = 106.38(1), = 90, C2/c, and a = 13.027(3) Å, b = 14.781(4) Å, c = 16.107(3) Å, = 90, = 105.30(1), = 90, P2₁/n; [(L1OH)Cd(pz)(NO₃)₂] a = 14.7476(2) Å, b = 13.5411(2) Å, c = 16.7223(2) Å, = 90, = 110.3840(10), = 90, P2₁/c; and [(L1O)Co(pz)(NO₃)] a = 11.4240(2) Å, b = 13.4498(2) Å, c = 13.8056(2) Å, = 105.2080(10), = 105.8130(10), = 112.7470(10), P . The Zn adopts a pseudotetrahedral four-coordinate geometry where the potentially tridentate ligand is actually bidentate with a protonated and uncoordinated phenoxy arm. The Co complex is pseudooctahedral six-coordinate where the phenoxy arm is deprotonated and coordinated. Finally the Cd complex is seven-coordinate but the metal is not coordinated through the phenoxy group that is again protonated.