Statistical Gambler's Ruin Problem

Abstract

The gambler's ruin problem is one of the most important problems in the emergence of probability. The problem has been long considered “solved” from a probabilistic viewpoint. However, we do not find the solution satisfactory. In this paper, the problem is recast as a statistical problem. Bounds of the estimate are derived over wide classes of priors. Interestingly, the probabilistic estimates ω(1/2) are identified as the most conservative solutions while the plug-in estimates are found to be out of range of the bounds. It implies that, although conservative, the probabilistic estimates ω(1/2) are justified by our analysis while the plug-in estimates are too extreme for estimating the ruin probability of gambler.     

A Unified Approach to Structural Change Tests Based on ML Scores,F Statistics,and OLS Residuals

This paper presents an easy-to-compute semi-parametric (SP) method to estimate a simple disequilibrium model proposed by Fair and Jaffee (1972). The proposed approach is based on a non-parametric interpretation of the EM (Expectation and Maximization) principle (Dempster et al; 1977) and the least squares method. The simple disequilibrium model includes the demand equation, the supply equation, and the condition that only the minimum of quantity demanded and quantity supplied is observed. The method used here allows one to consistently estimate the disequilibrium model without fully specifying the distribution of error terms in both demand and supply equations. Our Monte Carlo study suggests that the proposedestimator is better than the normal maximum likelihood estimator under asymmetric error distributions. and comparable to the nlaximunl likelihood estimator under synirnetric error distributions in finite samples. Aggregate U.S. labor market data from Quandt and Rosen (1988) is used to illustrate the procedure.     

Reliability and Some Characteristics of Circular Consecutive-k-Within-m-Out-of-n:F System

A system can be classified with respect to the physical arrangement of its components and the functioning principle. A circular consecutive k-within-m-out-of-n:F system consists of n circularly ordered components and fails if and only if there are m consecutive components that include among them at least k failed components. A circular consecutive k-within-m-out-of-n:F system turns into circular consecutive k-out-of-n:F for m = k and k-out-of-n:F system for m = n. In this study, signature-based analysis of circular consecutive k-within-m-out-of-n:F system is performed. A new approximation to this system is provided based on maximum number of failed components and an illustrative example is given for different values of n, m, k to compare the approximate results with simulated and exact results.     

Reliabilities for (n,f, k (i,j)) and ⟨n,f, k (i,j)⟩ Systems

The (n,f,k(i,j)):F(? n,f,k(i,j)?:F) system consists of n components ordered in a line or circle, while the system fails if, and only if, there exist at least f failed components OR (AND) at least k consecutive failed components among components i,i + 1,…,j ? 1,j. In this article, we present the system reliability formulae for these systems with product of matrices by means of a two-stage finite Markov chain imbedding approach, a technique first used by Cui et al. (2002 Cui , L. R. , Kuo , W. , Xie , M. ( 2002 ). On (f,g)-out-of-((i,j),n) systems and its reliability . In: Third International Conference on Mathematical Methods in Reliability Methodology and Practice , June 17–20 , Norway , Trondheim , pp. 173 – 176 . [Google Scholar]). In addition, their dual systems, denoted by (n,f,k(i,j)):G and ? n,f,k(i,j)?:G, are also introduced. Two numerical examples are given to illustrate the results.     

Two-stage tests of hypotheses in the general linear model

Two-stage (double sample) tests of hypotheses are presented for testing linear hypotheses in the general linear model. General and one-sided alternatives are considered. Computational techniques for computing critical points are discussed. Tables of critical points are presented. An example suggests that two-stage tests can achieve the same power as a fixed sample size test while reducing considerably the expected number of observations required for the test     

怎样深刻理解"三个代表"重要思想的历史地位

"三个代表"重要思想是系统的科学理论,是对马列主义、毛泽东思想、邓小平理论的继承和发展。党的十六大把"三个代表"确立为我们党必须长期坚持的指导思想,对于全面开创社会主义事业的新局面会产生积极重要的作用。     

The sensitivity of developing countries to external shocks in an interdependent world

North-South interdependence is illustrated by means of a general equilibrium model, in which the rural and urban sectors are treated entirely separately and urban real wages are downward rigid. We explain why such an approach may be more meaningful for long-run analysis than one that stresses the role of demand. The model's properties are illustrated by a theoretical analysis based on a simplified version of the system, and by simulations based on assumptions made by World Bank Staff in the 1983 World Development Report.     

Asset markets and foreign exchange intervention: A model of the Belgo-Luxemburg economic union

In this article a general formulation of government intervention policies in the foreign exchange market is integrated in the framework of an asset market model. The policy reaction function is based on a trade off between exchange rate and reserve stock fluctuations; constant exchange rates and a pure float are derived as limiting cases of the intervention schedule. An exchange rate equation is derived from the short run portfolio equilibrium of the model and is successfully tested using data for the Belgo-Luxemburg Economic Union (1967–1979). Our policy conclusions contrast the European Snake constraints for the Belgian Franc with Artus's findings (IMF Staff Papers XXIII(2), July 1976) for the leading DM.     

Macroeconomic imbalances in Europe: How to overcome the fallacy of unit labour costs

Policy recommendations based on unit labour costs (ULC) indices can lead to undesirable and counterproductive policies, because they do not reveal possible distortions in the base year. In this paper, we discuss the problems with the ULC-current account relation and provide an alternative measure for relative wage costs called Wage Competitive index (WCI) based on the assumption of convergence of the returns on capital. We show how to calculate it and that it is more efficient than traditional ULC and REER indicators. The implication is that policymakers should not focus on nominal wage setting only, but also more broadly on all factors which affect the return on capital. This implies that the well-known Rehn–Meidner rule, which underlies the Macroeconomic Dialogue should be modified.