A discrete and a continuous-time model based on a technical trading rule

In this article we propose a model in discrete and continuoustime that incorporates explicitly a technical trading rule inthe specification of the volatility. The proposed discrete-timemodel is an alternative to GARCH-type processes. We derive conditionsfor the covariance and strict stationarity of the discrete-timeprocess and we study the estimation and inference problems.We also analyze the conditions under which the discrete-timeprocess converges in distribution to a diffusion process. Toillustrate the proposed model and compare it with the GARCHspecification, we analyze the daily closing stock prices oftwo major U.S. companies (Microsoft and Oracle), two stock indices(DAX and NASDAQ) and two U.S. Dollar exchange rates (Euro andSterling)     

Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations

Maximum-likelihood estimates of the parameters of stochasticdifferential equations are consistent and asymptotically efficient,but unfortunately difficult to obtain if a closed-form expressionfor the transitional probability density function of the processis not available. As a result, a large number of competing estimationprocedures have been proposed. This article provides a criticalevaluation of the various estimation techniques. Special attentionis given to the ease of implementation and comparative performanceof the procedures when estimating the parameters of the Cox–Ingersoll–Rossand Ornstein–Uhlenbeck equations respectively.     

A note on the existence of unique equivalent martingale measures in a Markovian setting

Simple sufficient conditions for the existence of a unique equivalent martingale measure are provided. Furthermore, these conditions give us a handle on situations where an equivalent martingale measure cannot exist. The existence of a unique equivalent martingale measure is of relevance to problems in mathematical finance. Two examples of models for which the question of existence was unresolved are studied. By means of our results existence of a unique equivalent measure up to an explosion time is proved.     

A two-stage approach to defining an affected community based on the directly affected population and the sense of community

Studies have demonstrated the inadequacy of relying on existing administrative boundaries or simple proximity to define an affected community. The proposal and siting of hazardous facilities can have a range of impacts upon people across wide areas, with some more affected than others as a result of living with the physical impacts of construction or the fear associated with perceived risk. We term those most affected the directly affected population and propose a two-stage model for identifying an affected community which places those most affected at the centre of the definition. The second stage is to identify the relationships those most affected have with the wider elements of the sense of community to discover the existing community or communities which are affected. Illustrated by the siting of a low-level radioactive waste disposal facility at Dounrey in the north of Scotland, we show that elements of the lived community experience may have very different shapes, extents and conflicting interests which pose challenges for their incorporation into a siting process. The two-stage model presented in this paper, by placing those most directly affected at the centre and working from there out into the existing communities, identifies issues early in any siting process to improve their incorporation and amelioration.