Expected utility within a generalized concept of probability — a comprehensive framework for decision making under ambiguity

It has often been complained that the standard framework of decision theory is insufficient. In most applications, neither the maximin paradigm (relving on complete ignorance on the states of natures) nor the classical Bayesian paradigm (assuming perfect probabilistic information on the states of nature) reflect the situation under consideration adequately. Typically one possesses some, but incomplete, knowledge on the stochastic behaviour of the states of nature. In this paper first steps towards a comprehensive framework for decision making under such complex uncertainty will be provided. Common expected utility theory will be extended to interval probability, a generalized probabilistic setting which has the power to express incomplete stochastic knowledge and to take the extent of ambiguity (non-stochastic uncertainty) into account. Since two-monotone and totally monotone capacities are special cases of general interval probatility, wher Choquet integral and interval-valued expectation correspond to one another, the results also show, as a welcome by-product, how to deal efficiently with Choquet Expected Utility and how to perform a neat decision analysis in the case of belief functions. Received: March 2000; revised version: July 2001     

The symmetric and asymmetric Choquet integrals on finite spaces for decision making

In this paper, we give a mathematical analysis of symmetric and asymmetric Choquet integrals in the view of decision making in a finite setting. These integrals present two ways of dealing with negative integrands. The analysis is done with the aid of the Möbius and interaction transforms, this last one having an interesting interpretation in multicriteria decision making (MCDM). The last part of the paper shows the application of these two integrals in MCDM.     

Sharing beliefs and the absence of betting in the Choquet expected utility model

Choquet expected utility maximizers tend to behave in a more “cautious” way than Bayesian agents, i. e. expected utility maximizers. We illustrate this phenomenon in the particular case of betting behavior. Specifically, consider agents who are Choquet expected utility maximizers. Then, if the economy is large, Pareto optimal allocations provide full insurance if and only if the agents share at least on prior, i. e., if the intersection of the core of the capacities representing their beliefs is non empty. In the expected utility case, this is true only if they have a common prior. Received: July 2000; revised version: May 2001     

On the axiomatic treatment of the ϕ-mean

Summary We extend to masses on a real interval the notion of ϕ-mean, usually considered in the context of σ-additive probabilities or probability distribution functions, and consider some axiomatic treatments of it at different levels of masses (simple masses, compact support masses, tight masses, arbitrary masses). Moreover, as an important special case, we get axiomatic systems for general means, as well. We also prove that the usual axiomatic system “Consistency with Certainty+Associativity+Monotonicity” characterizes the ϕ-mean of masses with arbitrary compact support and that, already at tight masses level, this system is not adequate. We note that the analytical tool used to define the ϕ-mean is the Choquet integral. Work performed under the auspices of the National Group: “Inferenza Statistica: basi probabilistiche e sviluppi metodologici” (MURST 40%).     

社会保险缴费对企业雇佣工资和规模的影响研究

社会保险与劳动力市场就业和工资的关系备受关注,其本质在于社保缴费对企业雇佣工资和雇佣规模的影响。本文基于企业薪酬调查与第三次经济普查对接形成的“企业-员工”匹配数据,从企业雇佣决策的整体性出发,将缴费负担及其影响置于我国缴费监管的特殊制度背景之下,运用系统估计法模拟社保缴费对企业雇佣工资和雇佣规模的影响。研究发现：企业实际承担的社保缴费费率越高,其雇佣工资显著越低、雇佣规模显著越小,社会保险以降低工资和减少就业的方式对劳动力市场运行存在双重影响;从标准化回归系数看,缴费负担对雇佣工资的影响强于对雇佣规模的影响,但雇佣规模缩减不仅是劳动者就业机会的损失更是企业经营风险的积累,对劳动力市场的影响尤其需要关注;从雇佣工资影响的程度看,缴费负担极大部分由企业承担,雇佣规模因缴费负担而缩减是用工成本上升的直接体现;从雇佣工资影响的结构看,缴费负担对职工福利有显著负影响、对奖金津贴形式的工资部分有更强的负影响,进一步反映出缴费负担形成的成本压力不可轻视,成本压力持续积累对劳动力市场运行的影响将是深远的。鉴于我国社会保险制度费率偏高同时逃避费行为较普遍的事实,鉴于未来劳动工资上涨、劳动供给结构性乃至整体性相对不足的基本趋势,建议合理缴费负担,同时严格缴费执法,以此谋求社会保险制度与劳动力市场运行的有效协同。     

Some aspects of decision making under uncertainty

Two discrete-time insurance models are studied in the framework of cost approach. The models being non-deterministic one deals with decision making under uncertainty. Three different situations are investigated: (1) underlying processes are stochastic however their probability distributions are given; (2) information concerning the distribution laws is incomplete; (3) nothing is known about the processes under consideration. Mathematical methods useful for establishing the (asymptotically) optimal control are demonstrated in each case. Algorithms for calculation of critical levels are proposed. Numerical results are presented as well.     

Multivariate Chebyshev inequality in generalized measure space based on Choquet integral

The multivariate Chebyshev inequality for a random vector on probability measure space has been studied by numerous authors. One thing that seems missing is the multivariate version of Chebyshev inequality in non additive cases. In this article, we show that this inequality still works in generalized probability theory based on Choquet integral.     

中国社会发展水平综合评价研究

一、问题的提出自20世纪90年代以来,人类发展问题已成为当代社会人们研究的重大课题。诚然,人类社会是发展了,但发展的现实世界中还有许多不尽如人意之处。如经济发展了,却带来许多产品生产过剩的问题;人口平均寿命提高了,却又伴随着出现老龄人口的社会保障问题;经济发展的速度     

Variable Selection for Qualitative Interactions

In this article we discuss variable selection for decision making with focus on decisions regarding when to provide treatment and which treatment to provide. Current variable selection techniques were developed for use in a supervised learning setting where the goal is prediction of the response. These techniques often downplay the importance of interaction variables that have small predictive ability but that are critical when the ultimate goal is decision making rather than prediction. We propose two new techniques designed specifically to find variables that aid in decision making. Simulation results are given along with an application of the methods on data from a randomized controlled trial for the treatment of depression.     

Global benefit-risk assessment in designing clinical trials and some statistical considerations of the method

When characterizing a therapy, the efficacy and the safety are two major aspects under consideration. In prescribing a therapy to a patient, a clinician puts the two aspects together and makes a decision based on a consolidated thought process. The global benefit-risk (GBR) measures proposed by Chuang-Stein et al. (Stat. Med. 1991; 10:1349-1359) are useful in facilitating the thinking, and creating the framework for making statistical comparisons based on benefit-risk point of view. This article describes how a GBR linear score was defined and used as the primary outcome measure in a clinical trial design. The robustness of the definitions of 'benefit' and 'risk' are evaluated using different criteria. The sensitivity of the pre-specified weights is also analyzed using alternative weights; one of those was determined by the relative to an identified distribution integral transformation approach (Biometrics 1958; 14:18-38). Statistical considerations are illustrated using pooled data from clinical trials studying antidepressant. The pros and cons for using GBR assessments in the setting of clinical trials are discussed.     

我国企业社会保险逃费现象的实证检验

本文基于规模以上工业企业的普查数据,通过对比平均工资水平与企业实际缴纳社保以及公积金之间的关系,检验我国企业是否存在社保逃费现象。我们的实证结果表明,高工资企业实际缴纳社保比例相对较低,说明高工资企业具有更强的动机逃避社保费用;而作为参照,高工资企业虽然需要缴纳更高的住房公积金,但由于实际享受的公积金待遇也较高,企业及其员工并没有动机少缴公积金。本文建议应该从社保的筹资和补偿机制入手,进一步完善社保的多缴多得机制。     

社会保险与商业保险的结合方式及保险资金入市研究

 社会养老保险与个人储蓄养老保险同属社会保障范畴,其共同目标是通过保险基金的增值,为投保人提供稳定可靠的养老保障,以确保安全度过人口老龄化高峰期。多年来,我国社会养老保险与商业人寿保险囿于立法范畴、管理体制、性质、特点、作用、范围、权利与义务关系的相异性,两者互不相融,各自发展,不利于养老保障三大支柱的建立。如今,以保险基金入市为契机,以资本市场为纽带,实现社会养老保险与商业人寿保险的协调与发展,是未来社会保障改革的基本走势。     

Loss prediction in a linear model under a linear constraint

Loss reserving is an important subject of actuarial mathematics. It aims at the prediction of future losses caused by claims which have incurred in the past but have not yet been closed. The problem of predicting such losses is particularly important in liability insurance. In the present paper we study conjoint prediction of paid and incurred losses in a linear model with a linear constraint which is intended to reduce the gap between the predictors of ultimate paid and incurred losses. We thus present an application to actuarial mathematics of the general result established by Kloberdanz and Schmidt (AStA Adv. Stat. Anal. 92:207–215, 2008).     

医疗保险、社会资本与健康水平

中国经济发展的目标之一就是保障人民健康安全,实现这一目标必然要求从战略高度审视居民健康水平,把保障人民健康作为经济社会发展的基本优先目标。文章通过构建医疗保险、社会资本与健康水平的模型,采用2010—2018年CFPS五年的追踪数据,运用工具变量法,实证检验了医疗保险、社会资本与健康水平之间的相互关系。结果表明:医疗保险的参保类型会影响居民的健康水平,而在中国这样的传统型关系社会中,社会资本不仅对健康有着重要的影响,还可能加强或者减弱医疗保险对居民健康水平的影响。具体而言,"新农合"和认知性社会资本对居民健康有显著的正向作用,"城居保"和结构性社会资本对居民健康有显著的负向作用。进一步地,结构性社会资本对"新农合"产生正面影响起到了阻碍作用,却充当了"城居保"扩大负面影响的缓冲剂。     

Information and capacities

Most economists consider that the cases of negative information value that non-Bayesian decision makers seem to exhibit, clearly show that these models are not models representing rational behaviour. We consider this issue for Choquet Expected Utility maximizers in a simple framework, that is the problem of choosing on which event to bet. First, we find a necessary condition to prevent negative information vlaue that we call Separative Monotonicity. This is a weaker condition than Savage Sure thing Principle and it appears that necessity and possibility measures satisfy it and that we cand find conditioning rules such that the information value is always positive. In a second part, we question the way information value is usually measured and suggest that negative information values are merely resulting from an inadequate formula. Yet, we suggest to impose what appears as a weaker requirement, that is, the betting strategy should not be Statistically Dominated. We show for classical updating rules applied to belief functions that this requirement is violated. We consider a class of conditioning rules and exhibit a necessary and sufficient condition in order to satisfy the Statistical Dominance criterion in the case of belief functions. Received: November 2000; revised version: July 2001     

社会保障支出与拉动内需——对农村养老保障问题的深入探讨

本文通过实证分析,探讨了农村养老保障问题与拉动内需之间的关系。结果认为农村居民消费水平与抚恤和社会福利救济费、养老保险、行政事业单位离退休经费呈显著正相关,并且社会保障支出项目对农村居民消费的作用存在地区差异,农村居民养老保险对消费的促进作用存在区域差异。由此提出建立健全农村养老保险制度,可以作为我国拉动内需、促进经济增长的突破口。     

Statisticians Can Matter

Statisticians fall far short of their potential as guides to enlightened decision making in business. Two important explanations are: (1) Decision makers are often more easily convinced by concrete examples, however fragmentary and misleading, than by competent statistical analysis. (2) The effective use of statistics in the process of decision making requires hard thinking by decision makers, thinking that cannot be delegated entirely to the statistical specialist. Modern developments in interactive statistical computing may help to reduce the force of these limitations on exploitation of statistics; used properly, computing can encourage, almost force, the student or business user of statistics to think statistically.     

基于Pair-Copula的社保基金投资组合风险测度研究

社保基金是社会保障事业健康发展的基石,风险管理是社保基金保值增值的关键问题之一。提出pair—copula—GARCH—EVT模型以测度社保基金投资组合风险,与传统的n维。copula—GARCH—EVT模型相比,该模型不仅考虑了维数的影响,而且还能灵活地选择copula的类型。实证研究发现,基于pair—cOpula—GARCH--EVT模型测度社保基金投资组合风险的准确性要高于传统的copuIa--GARCH--EVT模型。     

Clinical utility estimation for assay cutoffs in early phase oncology enrichment trials

Predictive enrichment strategies use biomarkers to selectively enroll oncology patients into clinical trials to more efficiently demonstrate therapeutic benefit. Because the enriched population differs from the patient population eligible for screening with the biomarker assay, there is potential for bias when estimating clinical utility for the screening eligible population if the selection process is ignored. We write estimators of clinical utility as integrals averaging regression model predictions over the conditional distribution of the biomarker scores defined by the assay cutoff and discuss the conditions under which consistent estimation can be achieved while accounting for some nuances that may arise as the biomarker assay progresses toward a companion diagnostic. We outline and implement a Bayesian approach in estimating these clinical utility measures and use simulations to illustrate performance and the potential biases when estimation naively ignores enrichment. Results suggest that the proposed integral representation of clinical utility in combination with Bayesian methods provide a practical strategy to facilitate cutoff decision‐making in this setting. Copyright © 2015 John Wiley & Sons, Ltd.     

流动人口的社会保险覆盖率及其影响因素分析

利用国家卫计委2010年12月的全国性大规模调查数据,本文研究了城市外来流动人口的社会保险覆盖率及其影响因素。研究发现,教育和培训提高了流动人口的参保概率;企业所有制性质、有无劳动合同,显著影响流动人口的参保;农民工各项社会保险的参保状况显著低于城城流动人口,并且中部地区流动人口的社会保险参保率显著低于东部和西部地区。流动人口不再是被动的社会保险获得者,已经有了一定的主动权。在提高流动人口社会保险覆盖率的政策设计上,除了加强流动人口的职业培训和教育之外,还应该严格落实新《劳动合同法》的实施,将农民工作为社会保险扩面工程的重点人群,并将中部地区作为扩面工程的重点区域。