A resolution of St. Petersburg paradox

The St. Petersburg paradox is the oldest paradox in decision theory and has played a pivotal role in the introduction of increasing concave utility functions embodying risk aversion and decreasing marginal utility of gains. All attempts to resolve it have considered some variants of the original set-up, but the original paradox has remained unresolved, while the proposed variants have introduced new complications and problems. Here a rigorous mathematical resolution of the St. Petersburg paradox is suggested based on a probabilistic approach to decision theory.     

Equilibrium storage with multiple commodities

This paper introduces a multisector model of commodity markets with storage, where equilibrium is defined by profit maximization, arbitrage and market clearing conditions. We then solve for the decentralized equilibrium via a corresponding dynamic program. We also describe the dynamics of the model, establishing geometric ergodicity, a Law of Large Numbers and a Central Limit Theorem.     

AN INFRA-SURFER'S PARADISE: RIDING THE CREST OF THE LAND - VALUE WAVE

The author devoted his working life to adding wealth to the nation. Now, to expose the damage caused by taxes to the enterprise economy, he is an accredited Infra-surfer. And as he triangulates between deals in St Petersburg, up-state New York and the coast of Spain, he finds himself slipping into a dream-like world of virtual reality…     

Dynamics of the Standard of Living in St Petersburg during Five Years of Economic Reform

The monitoring of changing living conditions in St Petersburg was started in 1989. In 1993 the Finance and Economics Committee of the Government of St Petersburg and a team of researchers from the Institute of Sociology at the Russian Academy of Sciences began collaborating in a study of the levels of socio-economic differentiation among the population and the priorities in city budget policies. A telephone survey scheme was designed based on representative samples (1000–2500 respondents) of the adult population (18 years and over) and controlled by city district distribution, sex, age, social status and housing. This scheme was implemented regularly with 2–3 month intervals between surveys. It was also undertaken for the purpose of reviewing the general orientation of social politics, decisions on budget priorities, new urgent needs and goals, and the diagnosis and short-term prognosis of trends and policy moves. Detailed and structured information on the living standards of the St Petersburg population is available from the computerized data-base, reports, and from the city's daily newspaper Nevskoe vremya. The studies have demonstrated that economic differentiation in St Petersburg has grown significantly as a result of current reforms (from a 1 to 4 ratio before 1990 to 1 to 10 by the end of 1996). Analysis of the economic characteristics of the population of St Petersburg has revealed that over the course of the past five years there has been rapid differentiation along new lines. At present, wealth and poverty, rather than shared social and professional attributes, tend to unite or separate people. The level of family and personal income determines consumer behaviour, lifestyle, values, cultural attitudes and even individuals' self-perception. La surveillance des changements des conditions de vie à Saint Pétersbourg a commencé en 1989. En 1993 le Comité de l'Economie et des Finances du Gouvernement de Saint Pétersbourg et une équipe de chercheurs de l'Institut de Sociologie de l'Académie des Sciences de Russie commencèrent une étude collaborative des niveaux de différenciation socio-économique dans la population et des priorités de la politique budgétaire de la ville. Un sondage téléphonique fut proposé, fondé sur une section représentative (1000 à 2500 personnes) de la population adulte (de 18 ans et plus) et contrôllée par la distribution des quartiers de la ville, par sexe, âge, statut social et logement. Ce projet fut mis en exécution régulièrement, avec 2 ou 3 mois d'intervalle entre les sondages. Il fut aussi entrepris dans le but d'examiner l'orientation générale des politiques sociales, des décisions quant aux priorités budgétaires, les nouveaux besoins et buts urgents, et le diagnosis et prognosis à court terme des tendances et changements de politique. L'information détaillée structurée concernant les niveaux de vie de la population de Saint Pétersbourg peut être obtenue dans le compte-rendu de la base des donnés sur l'ordinateur et dans le quotidien de la ville, Nevskoe Vremya. Les recherches ont démontré que le différenciation économique à Saint Pétersbourg a considérablement augmentéà la suite des réformes actuelles (d'une proportion de 1 à 4 avant 1990 à une proportion de 1 à 10 à la fin de 1996). L'analyse des caractéristiques économiques de la population de Saint Péterbourg a révélé qu'il y a eu une rapide différenciation d'un type nouveau au cours des cinq dernières années. A présent ce sont la richesse et la pauvreté, plutôt que les attributs sociaux et professionnels communs, qui ont tendance à unir ou à séparer les gens. Le niveau de revenu personnel et familial détermine le comportment des consommateurs, le style de vie, sens des valeurs, attitudes culturelles et même la perception d'eux-mêmes qu'ont les individus.     

Urban government: a focal issue in studies on the Russian and Soviet city

Book reviewed in this article: Bater, J. H. 1976: St Petersburg. Industrialization and change. Hamm, M. F. , editor, 1976: The city in Russian history. Davidow, M. 1976: Cities without crises.     

The Law and Economics of Historic Preservation in St. Petersburg, Russia

St. Petersburg's architectural heritage makes it one of the most beautiful cities in Russia. However, as government subsidies continue to dwindle, the city is increasingly dependent upon private sources of financing to restore and preserve the many seriously deteriorated monuments and buildings. This article considers whether the economic and legal environment in St. Petersburg provides sufficient incentives for private investors to undertake historic rehabilitation projects. A pro forma model is used to analyze a developer's return on investment in new residential construction on the outskirts of the city versus rehabilitation of an historic residential building. The results show that the costs associated with historic preservation are significantly greater than for new construction and for a developer to make a reasonable rate of return on historic preservation the square meter price of residential space would be affordable by only a small segment of the population. Simultaneous changes to multiple legal and economic policies are recommended to encourage additional private investment in historic preservation.     

Dirt: Symbolic and Practical Dimensions of Social Problems in St Petersburg

Our article deals with the representation of social problems by ordinary families in St Petersburg. We try to answer two questions: How are statements about social problems constructed? What are the citizens of St Petersburg referring to when they talk about social problems? Our material consists of loosely structured thematic interviews with 42 families in St Petersburg in 1993. The interviews were part of a joint Finnish-Russian study on living conditions, survival strategies, social problems and social networks in Russia. The title of our paper comes from the somewhat surprising observation that dirt and disorder in everyday life were the most frequently mentioned social problems. These and other statements made about social problems in present-day Russia are taken as examples of social constructs and it is argued that these privately produced claims should be conceived as part of the public claims-making process within the constructionist tradition. Instead of the traditional four-field (private/public intersecting with the symbolic/practical) scheme, however, we suggest a more complex ‘hexagon’ scheme, in order to emphasize that the speaker as a subject employs multiple identities (various conceptions of ‘me’ and ‘us’) simultaneously. The hexagon model enables us to analyse the scattered references to dirt in a unifying framework of concepts. In answer to the question of why dirt is perceived to be such an important social problem for the citizens of St Petersburg it is concluded that dirt (like other identified social problems) is a multi-dimensional phenomenon that refers on a practical and symbolic level to a variety of larger concerns. Notre article concerne la représentation des problèmes sociaux par les familles ordinaires de Saint Pétersbourg. Nous essayons de répondre à deux questions: Comment sont construites les formulations des problèmes sociaux? De quoi parlent les citoyens de Saint Pétesbourg quand ils parlent de problèmes sociaux? Notre matériel se compose des interviews thématiques à structure flexible de 42 familles de Saint Pétersbourg faites en 1993. Ces interviews faisaient partie d'une étude conjointe finlandaise et russe sur les conditions de vie, les stratagèmes de survie, les problèmes et les réseaux sociaux en Russie. Le titre de notre article provient de l'observation quelque peu surprenante que la saleté et le désordre dans la vie de tous les jours sont les problèmes sociaux les plus couramment cités. Ces formulations des problèmes sociaux dans la Russie actuelle sont prises comme exemples de constructions sociales, et nous soutenons que ces demandes produites en privé doivent être con¸ues comme faisant partie des demandes publiques dans la tradition constructiviste. A la place du modèle traditionnel à quatre champs (le public/privé recoupant le symbolique/pratique), nous suggérons un modèle ‘hexagone’ plus complexe afin de souligner que la personne qui parle, en tant que sujet, utilise simultanément des identités multiples (plusieurs concepts de ‘moi’ et ‘nous’). Le modèle ‘hexagone’ nous permet d'analyser les allusions à la saleté, bien que dispersées, dans une structure de concepts unifiée. En réponse à la question de savoir pourquoi la saleté est per¸ue comme un problème social d'une telle importance par les citoyens de Saint Pétersbourg, nous concluons est que la saleté (comme les autres problèmes sociaux identifiés) est un phénomène à plusieurs dimensions qui se rapporte à une variété de problèmes plus généraux au niveau pratique et symbolique.     

Validating an agent-based model of the Zipf׳s Law: A discrete Markov-chain approach

This study discusses the validation of an agent-based model of emergent city systems with heterogeneous agents. To this end, it proposes a simplified version of the original agent-based model and subjects it to mathematical analysis. The proposed model is transformed into an analytically tractable discrete Markov model, and its city size distribution is examined. Its discrete nature allows the Markov model to be used to validate the algorithms of computational agent-based models. We show that the Markov chains lead to a power-law distribution when the ranges of migration options are randomly distributed across the agent population. We also identify sufficient conditions under which the Markov chains produce the Zipf׳s Law, which has never been done within a discrete framework. The conditions under which our simplified model yields the Zipf׳s Law are in agreement with, and thus validate, the configurations of the original heterogeneous agent-based model.     

MEASURING MACROECONOMIC INSTABILITY: A CRITICAL SURVEY ILLUSTRATED WITH EXPORTS SERIES

For at least 40 years, the analysis of the causes and consequences of macroeconomic instability has greatly deepened our understanding of the handicaps faced by developing countries. This concern on economic instability is evidenced by a broad spectrum of indicators, based on the deviation of observed values of a given economic aggregate from its reference or trend value. In general, the choice of this or that indicator is not discussed advocating that the resulting instability indicators are closely correlated. Focusing on measurements of instability in export revenue data for 134 countries from 1970 to 2005, this paper finds that this assertion may be true for variance‐based indicators, measuring the average magnitude of deviations from the trend. However, great discrepancies may arise between different measures of the asymmetry or of the occurrence of extreme deviations around the trend when different trend computation methods are used. Our purpose is, therefore, to invite further discussions regarding the use of these indicators, and to highlight the different dimensions of instability, which have been so far unheeded by the economic literature.     

Unconditional tests for association in 2 × 2 contingency tables in the total sum fixed design

The asymptotic approach and Fisher's exact approach have often been used for testing the association between two dichotomous variables. The asymptotic approach may be appropriate to use in large samples but is often criticized for being associated with unacceptable high actual type I error rates for small to medium sample sizes. Fisher's exact approach suffers from conservative type I error rates and low power. For these reasons, a number of exact unconditional approaches have been proposed, which have been seen to be generally more powerful than exact conditional counterparts. We consider the traditional unconditional approach based on maximization and compare it to our presented approach, which is based on estimation and maximization. We extend the unconditional approach based on estimation and maximization to designs with the total sum fixed. The procedures based on the Pearson chi‐square, Yates's corrected, and likelihood ratio test statistics are evaluated with regard to actual type I error rates and powers. A real example is used to illustrate the various testing procedures. The unconditional approach based on estimation and maximization performs well, having an actual level much closer to the nominal level. The Pearson chi‐square and likelihood ratio test statistics work well with this efficient unconditional approach. This approach is generally more powerful than the other p‐value calculation methods in the scenarios considered.     

A brigade model for the management of service volunteers: lessons from the former Soviet Union

This is a case study of a volunteer programme in a community welfare centre in St Petersburg, Russia. It is suggested that the successful and long‐term activation of its 900 volunteers can be credited to the programme's structural and managerial characteristics. These include: a formal and hierarchical structure and management; clearly defined privileges and obligations; small working groups called ‘brigades’; a comprehensive support system for volunteers and a variety of volunteer opportunities and participation benefits. Advantages and limitations of the programme are discussed, as well as the applicability of some of its principles to other settings. The research demonstrates the importance of contextual and socio‐cultural variables to the debate on the relevance to volunteer work of managerial principles applied with paid employees. Copyright © 2004 Henry Stewart Publications     

Bayesian Calibration of p‐Values from Fisher's Exact Test

p‐Values are commonly transformed to lower bounds on Bayes factors, so‐called minimum Bayes factors. For the linear model, a sample‐size adjusted minimum Bayes factor over the class of g‐priors on the regression coefficients has recently been proposed (Held & Ott, The American Statistician 70(4), 335–341, 2016). Here, we extend this methodology to a logistic regression to obtain a sample‐size adjusted minimum Bayes factor for 2 × 2 contingency tables. We then study the relationship between this minimum Bayes factor and two‐sided p‐values from Fisher's exact test, as well as less conservative alternatives, with a novel parametric regression approach. It turns out that for all p‐values considered, the maximal evidence against the point null hypothesis is inversely related to the sample size. The same qualitative relationship is observed for minimum Bayes factors over the more general class of symmetric prior distributions. For the p‐values from Fisher's exact test, the minimum Bayes factors do on average not tend to the large‐sample bound as the sample size becomes large, but for the less conservative alternatives, the large‐sample behaviour is as expected.     

用期权定价模型评估企业并购的价值

针对传统企业并购价值评估模型的局限性,本文从期权的角度阐述了企业并购的期权特性,指出企业并购实质上相当于取得了一个看涨期权;并以连续支付红利的美式期权定价理论为基础,建立了企业并购价值评估的期权定价模型。最后,通过实例论述了如何应用该模型来评估企业并购价值,对实践中企业并购价值的合理确定具有重要的指导意义。     

The Statistical Education of Harold Jeffreys

The paper considers the statistical work of the physicist Harold Jeffreys. In 1933–4 Jeffreys had a controversy with R.A. Fisher, the leading statistician of the time. Prior to the encounter, Jeffreys had worked on probability as the basis for scientific inference and had used methods from the theory of errors in astronomy and seismology. He had also started to rework the theory of errors on the basis of his theory of probability. After the encounter Jeffreys produced a full-scale Bayesian treatment of statistics in the form of his Theory of Probability.     

Ladislaus von Bortkiewicz—Statistician,Economist and a European Intellectual

Ladislaus von Bortkiewicz (1868–1931) was a European statistician. His scientific work covered theoretical economics, stochastics, mathematical statistics and radiology; today, we would call him a cross‐disciplinary scientist. With his clear views on mathematical principles with their applications in these fields, he stood in conflict with the mainstream economic schools in Germany at the dawn of the 20th century. He had many prominent students (Gumbel, Leontief and Freudenberg among them), and he carved out the path of modern statistical thinking. He was a true European intellectual with a career path from St. Petersburg via Göttingen to Straßburg and finally the Berliner Universität, now Humboldt‐Universität zu Berlin. He is known for the precise calibration of insurance claims applying the—at that time hardly known—Poisson distribution to Prussian horse kick and child suicide data. He proposed a simple solution to the Marxian transformation problem and wrote numerous articles and books on the mathematical treatment of statistical (including radiological physical) data. In this article, we sketch his life and work and point out the prominent role that he has in today's statistical thinking.     

Boekbesprekingen

Book reviewed in this article:
"Netwerkplanning volgens PERT", Oorspronkelijke uitgave Federal Electric Corporation. Voor Nederland bewerkt door H. POOLMAN Jr en TH. M. FEMER.
Group representations and applied probability, E. J. HANNAN
Wahrscheinlichkeit und Information, A. M. YAGLOM und J. M. YAGLOM
Linear programming and the theory of the Arm, K. E. BOULDING en W. A. SPIVEY
Einftihring in die matbematische Statistik, L. SCHMETTERER
Recent results in information theory, S. KOTZ
Formeln und Tabellen der mathematischen Statistik, U. GRAF, H. J. HENNINO en K. STANGE
The elements of probability theory and some of its applications, H. CRAMER
Quality control and industrial statistics, ACHESON J. DUNCAN
Méthodes Statistiques de ľéonometrie, E. MALINVAUD
Wahrscheinlichkeitstheorie, H. RICHTER
Linear statistical inference and its applications, C. R. RAO, Wiley
Gebouw en getal - capita aselecta uit het bouwen en de statistiek, aangeboden aan JAN VAN ETTINGER
The Mathematical Approach to Biology and Medicine, NORMAN T. J. BAILEY
Zum Problem der Produktionsplanung in Ein- und Mehrproduktunternehmen, W. DINKEL-BACH
[1] Die grundlagen der Theorie der Markoffschen Prozesse, E. B. DYNKYN
[1a] Theory of Markov processes, E. B. DYNKYN
[1b] Markov Processes, 2 delen, E. B. DYNKYN
[2] Probability and related topics in physical sciences, M. KAC, Interscience publ., London, 1959.
[3] Markov chains with stationary transition probabilities, K. L. CHUNG
[4] Probabilités et potentiel, P. A. MEYER
[4a] Probability and potentials, P. A. MEYER
[4b] Processus de Markov, P. A. MEYER
[5] Intégration, N. BOURBAKI
[6] Principles of random walk, F. SPITZER
[7] An introduction to probability theory and its applications, second edition, W. FELLER     

企业并购风险问题研究

从20世纪90年代并购在我国发展很快,并购不再是企业扭亏为盈的手段,已经成为企业资本运营的重要手段。但并购是一把“双刃剑”并购也存在着很多风险,本文从并购风险的形成动因,并购风险的种类,衡量并对其进行了实证研究,最后提出了风险防范的措施。以期为并购者提供借鉴,在并购中做出正确的决策,做好各风险的防范,达到并购的效果。     

Exact sampling from anti-monotone systems

A new approach to Markov chain Monte Carlo simulation was recently proposed by Propp and Wilson. This approach, unlike traditional ones, yields samples which have exactly the desired distribution. The Propp–Wilson algorithm requires this distribution to have a certain structure called monotonicity. In this paper an idea of Kendall is applied to show how the algorithm can be extended to the case where monotonicity is replaced by anti-monotonicity. As illustrating examples, simulations of the hard-core model and the random-cluster model are presented.     

企业并购财务风险分析与控制

企业并购对于优化资产结构、加速企业的发展有重要意义。企业购并发生后,企业的经营状况、资本结构将发生巨大变化,进而产生企业购并经营风险和财务风险。本文对企业购并风险出现形式进行了探讨,并为控制企业并购财务风险建立财务规划,通过资本结构设计、现金预算控制企业并购财务风险。     

马尔可夫性及其检验方法研究

马尔可夫链广泛应用于信息论、自动控制、通信技术、基因遗传、计算机科学、经济管理、教育管理、市场预测等领域,马尔可夫性是其最基本特征,因此,在运用马尔可夫链进行预测时,必须对预测对象以往的统计数据资料构成的随机变量序列的马尔可夫性进行检验,只有符合马尔可夫性,才能利用马尔可夫链进行预测,才能保证预测精度。本文探讨了马氏性的概念及性质,研究了马尔可夫性的检验方法,通过实例对该检验方法进行了分析。