Volume 24 - Issue 1 - June 1999

Thackeray and the Belgian progression

S. N. Ethier

Abstract

It is argued that the `Contrebanque de Noirbourg' episode in Thackeray's 1850 Christmas book, The Kickleburys on the Rhine, was based on an actual event, and that the `infallible system for playing rouge et noir' was in fact le montant belge, or the Belgian progression. This gambling system can be modeled by a three-dimensional Markov chain, which can in turn be reduced to a two-dimensional one. Assuming a house limit, probabilities and expectations of interest are evaluated in terms of the two-dimensional chain by means of a recursive algorithm. In the absence of a house limit, the system is analysed by classifying the three-dimensional chain, and its asymptotic behavior is studied in the transient case.

Stable Paretian models in econometrics: part I

S. T. Rachev, J-R. Kim and S. Mittnik

Abstract

We survey some recent results on econometric and time series modelling under the stable non-Gaussian hypothesis. It is widely accepted that the Gaussian assumption is too restrictive to model financial and other important macroeconomic variables, because their distributions exhibit asymmetry and heavy tails. In this paper we investigate empirical evidence for heavy-tailedness and skewness in economic variables, provide sampling distributions based on the Paretian random variables and throw light on some econometric issues such as outliers, structural breaks, and non-linearities from the viewpoint of the Paretian assumption. To do this, we generalize or modify estimators, statistics for hypothesis testing, and investigate their asymptotic distributions.

Optimal isolation policies for controlling two competing diseases

E. G. Kyriakidis

Abstract

This paper is mainly concerned with the problem of controlling a two-dimensional simple deterministic epidemic process in which one of the diseases is serious while the other is relatively harmless. Policies for isolating infectives with the serious disease are considered. For a suitable cost structure, the optimal policy which minimises the future cost for every initial state, is found. The corresponding stochastic model is also considered and a dynamic programming algorithm is found for determining the optimal policy, which at any stage minimises the expected future cost within a restricted class of policies. The optimal policies for the deterministic and stochastic models are compared numerically. An ecological interpretation of the models is also suggested.